A heave motion compensation system (3;103) for use with an offshore hoisting device, the heave motion compensation system (3;103) comprising: i. a heave compensation cylinder (9;109), having a piston (12;112), which heave compensation cylinder (9;109) is to be connected to a gas buffer (13;113) for providing the offshore hoisting device with passive heave compensation; ii. a sheave head (10;110), comprising one or more sheaves for engaging a hoisting wire (15;115) of the offshore hoisting device, wherein the sheave head (10;110) is supported by the piston (12;112) for movement along a heave compensation trajectory (16;116); iii. a sheave head track (11;111), extending parallel to the heave compensation trajectory (16;116); the heave motion compensation system (3;103) being further provided with a heave compensation adjusting system (17;117), the adjusting system comprising: i. an adjusting winch (18;118) with an associated adjusting wire (19;119); ii. a control device (23, 123), which control device is adapted to control the speed of the adjusting winch (18, 118, 118'), characterised in that the heave compensation adjustment system further comprises: iii. a trolley (20, 120), which trolley is coupled to the piston (12;112) of the heave compensation cylinder (9;109), preferably to the sheave head (10;110) supported by the piston (12;112) of the heave compensation cylinder (9;109), via a connector device and is coupled to the adjusting winch (18;118) via the adjusting wire (19;119), iv. a trolley track (21;121), which trolley track extends parallel and adjacent to the heave compensation trajectory (16;116); v. one or more sheaves (22;122), located at an end of the trolley track (21; 121), for guiding the adjusting wire (19;119,119') in a loop along the trolley track (21;121, 121), such that the adjusting winch (18;118) can pull the trolley (20;120), and thus the piston (12;112) of the heave compensation cylinder (9;109), in opposite directions along the heave compensation trajectory. i. a heave compensation cylinder (9;109), having a piston (12;112), which heave compensation cylinder (9;109) is to be connected to a gas buffer (13;113) for providing the offshore hoisting device with passive heave compensation; ii. a sheave head (10;110), comprising one or more sheaves for engaging a hoisting wire (15;115) of the offshore hoisting device, wherein the sheave head (10;110) is supported by the piston (12;112) for movement along a heave compensation trajectory (16;116); iii. a sheave head track (11;111), extending parallel to the heave compensation trajectory (16;116); i. an adjusting winch (18;118) with an associated adjusting wire (19;119); ii. a control device (23, 123), which control device is adapted to control the speed of the adjusting winch (18, 118, 118'), iii. a trolley (20, 120), which trolley is coupled to the piston (12;112) of the heave compensation cylinder (9;109), preferably to the sheave head (10;110) supported by the piston (12;112) of the heave compensation cylinder (9;109), via a connector device and is coupled to the adjusting winch (18;118) via the adjusting wire (19;119), iv. a trolley track (21;121), which trolley track extends parallel and adjacent to the heave compensation trajectory (16;116); v. one or more sheaves (22;122), located at an end of the trolley track (21; 121), for guiding the adjusting wire (19;119,119') in a loop along the trolley track (21;121, 121), such that the adjusting winch (18;118) can pull the trolley (20;120), and thus the piston (12;112) of the heave compensation cylinder (9;109), in opposite directions along the heave compensation trajectory.