This paper studies the forward kinematics of a sinking winch mechanism, which is in category of four-cable-driving parallel robot. The tension states (tautness or slackness) of cables are firstly taken into consideration in the forward kinematics model. We propose a traversal algorithm to solve the model. Both pose of platform and the tensions in cables can be solved if the lengths of four cables are given. The effectiveness of the algorithm is demonstrated by three examples. The results of this paper can be used to measure the pose of platform and the tensions of cables from the lengths of four cables.