The invention relates to the field of drilling well equipment, and provides a floating type drilling well heave compensation device. The floating type drilling well heave compensation device comprises a control table, a travelling block assembly, a big hook assembly, a passive compensation assembly, an active compensation assembly and a displacement detection device, wherein the passive compensation assembly and the active compensation assembly are arranged between the traveling block assembly and the big hook assembly in a way capable of performing telescopic movement, and are electrically connected with the control table. In the work process of the floating type drilling well heave compensation device, the travelling block assembly and the big hook assembly are connected in a relatively movable way through the passive compensation assembly and the active compensation assembly. When a load born by the big hook assembly changes, a piston rod of a passive compensation cylinder can correspondingly extend out or retract along with the load change; a passive energy storage device provides the corresponding pressure; and the displacement compensation is performed on a drilling column. Meanwhile, after the displacement detection, the control table outputs a control signal to control an active energy storage device to provide the pressure so that an active compensation cylinder extends or retracts the corresponding displacement for auxiliary compensation.