A wave energy converter, comprising a buoyant body, an acceleration tube suspended from and attached to the buoyant body and having an upper end adjacent to the buoyant body and a lower end at a distance from the buoyant body, wherein a portion of the acceleration tube defines a working cylinder between the upper end and the lower end, upper and lower openings in the acceleration tube for allowing a substantially unimpeded flow of water between the working cylinder and a body of water in which the acceleration tube is at least partially submerged when the wave energy converter operates as a result of wave movements, a working piston reciprocable in the working cylinder, a mooring system adapted to maintain the wave energy converter within a desired anchoring area and comprising at least one fastening device (110; 110') mounted on the buoyant body for attachment of a mooring line (111; 111') to the buoyant body, and an energy conversion assembly comprising at least one energy collecting device collecting energy from the movements of the working piston relative to the buoyant body resulting from said wave movements, characterized in that the energy collecting device includes a hydraulic piston pump in the form of a differential cylinder (116; 216) having an internal pump piston (117; 217), which is connected to the working piston in the acceleration tube via a piston rod (118; 218), wherein the differential cylinder (116; 216) comprises a substantially cylindrical pumping chamber (119; 219) on one side of the pump piston (117; 217) and an annular gap-shaped pumping chamber (120; 220) around the piston rod (118; 218) on the other side of the pump piston (117; 217), that the annular gap-shaped pumping chamber (120; 220) is adapted to be connectable, via hydraulic fluid conduits (121a, 121b, 121c, 121d, 121e; 221a), to a hydraulic pressure accumulator, and to then be further connectable, via hydraulic fluid conduits (121f, 121g, 121h), to a hydraulic motor in driving connection with a generator during operation of the wave energy converter, that a fluid connection provided with a one-way valve (126; 226) is arranged for connection between the cylinder chambers on each side of the pump piston (117; 217), from the substantially cylindrical pumping chamber (119; 219) to the annular gap-shaped pumping chamber (120; 220), that a fluid conduit (121j; 221j) provided with a one-way valve (127; 227) is arranged from a fluid tank to the substantially cylindrical pumping chamber (119; 219), so that, during operation of the wave energy converter, the pump piston (117; 217) will expel hydraulic fluid from the annular gap-shaped pumping chamber into the fluid conduits (121a, 121b, 121c, 121d, 121e; 221a) in a direction toward the pressure accumulator and simultaneously draw hydraulic fluid, via the fluid conduit (121j; 221j) from the fluid tank, into the substantially cylindrical pumping chamber (119; 219), during a working stroke causing a decrease in volume of the annular gap-shaped pumping chamber (120; 220), and so that the pump piston (117; 217), during a working stroke causing a decrease in volume of the substantially cylindrical pumping chamber (119; 219), will cause hydraulic fluid to bypass the pump piston (117; 217) through the fluid connection provided with the one-way valve (126; 226), from the substantially cylindrical pumping chamber (119; 219) into the annular gap-shaped pumping chamber (120; 220) and further in a direction toward the pressure accumulator via the fluid conduits (121a, 121b, 121c, 121d, 121e; 221a).