A fuel pump for supplying fuel to an internal combustion piston engine, comprising: a body and a cylindrical space arranged in the body having a central axis, a piston member arranged to reciprocate in the cylindrical space, where the cylindrical space comprises a first space section having a first diameter in which the wall of the space and the wall of the piston member are arranged against each other providing a first sealing gap such that the wall of the space guides the piston member in the body, and where the first space section is bordered by a first end of the piston member forming a first pumping chamber of the fuel pump configured to pump the fuel as the piston member reciprocates in the space, and where the cylindrical space further comprises a second space section (30") on the central axis having a second diameter greater than the first diameter, and where the piston member is provided with a sleeve member extending towards the first end of the piston member such that an annular space is provided between the sleeve member and the piston member, which annular space opens towards the first end of the piston member, and where an inner wall of the second space section (30") and a radially outer wall of the sleeve member are arranged against each other providing a second sealing gap such that the inner wall of the second space section guides the sleeve member in the second space section (30"), and wherein the pump body is provided with a cylindrical extension which is coaxial to the first space section forming an annular gap circumscribing the piston member, wherein the sleeve member is arranged to extend into the annular gap between the cylindrical extension and inner wall of the second space section (30"), wherein an annular third space section is arranged into fuel pump which third space section is partially bordered by the inner wall of the second space section (30"), the outer wall of the cylindrical extension and the sleeve member which is arranged to extend into the annular third space section, characterised in that the second space section (30") is provided with a second pumping chamber of the pump configured to pump fuel from the second space section (30"), as the piston member reciprocates in the space, and the pump is provided with a vent flow path connecting the second space section (30") to outside of the body for allowing gas admission into the second space section (30"), driven by the reciprocating movement of the piston member, and a discharge flow path connecting the second space section (30") to outside of the body for transferring fuel material away from the second space section (30"), and in that a lubrication oil supply channel and a lubrication oil discharge channel are connected to the third space section. a body and a cylindrical space arranged in the body having a central axis, a piston member arranged to reciprocate in the cylindrical space, where the cylindrical space comprises a first space section having a first diameter in which the wall of the space and the wall of the piston member are arranged against each other providing a first sealing gap such that the wall of the space guides the piston member in the body, and where the first space section is bordered by a first end of the piston member forming a first pumping chamber of the fuel pump configured to pump the fuel as the piston member reciprocates in the space, and where the cylindrical space further comprises a second space section (30") on the central axis having a second diameter greater than the first diameter, and where the piston member is provided with a sleeve member extending towards the first end of the piston member such that an annular space is provided between the sleeve member and the piston member, which annular space opens towards the first end of the piston member, and where an inner wall of the second space section (30") and a radially outer wall of the sleeve member are arranged against each other providing a second sealing gap such that the inner wall of the second space section guides the sleeve member in the second space section (30"), and wherein the pump body is provided with a cylindrical extension which is coaxial to the first space section forming an annular gap circumscribing the piston member, wherein the sleeve member is arranged to extend into the annular gap between the cylindrical extension and inner wall of the second space section (30"), wherein an annular third space section is arranged into fuel pump which third space section is partially bordered by the inner wall of the second space section (30"), the outer wall of the cylindrical extension and the sleeve member which is arranged to extend into the annular third space section, characterised in that the second space section (30") is provided with a second pumping chamber of the pump configured to pump fuel from the second space section (30"), as the piston member reciprocates in the space, and the pump is provided with a vent flow path connecting the second space section (30") to outside of the body for allowing gas admission into the second space section (30"), driven by the reciprocating movement of the piston member, and a discharge flow path connecting the second space section (30") to outside of the body for transferring fuel material away from the second space section (30"), and in that a lubrication oil supply channel and a lubrication oil discharge channel are connected to the third space section.