In this paper, adaptive control method is presented for a parallel cable with six degrees of freedom and six cable. Adaptive control method is a way for controlling systems that there is uncertainty in the parameters. The main objective of this study is tracking trajectory of a parallel cable robot which there is uncertainty in the mass of end effector and moments of inertia. Before addressing the issue of control, Jacobian matrix of robot is obtained. Then the dynamic equations of motion are derived using Lagrange method and is written in standard form. The presented adaptive control method is combination of feedback linearization method and Lyapunov stability theorem. Using feedback linearization method, control law is designed and adaptation law is planned by use of Lyapunov stability theorem. Due to the unique feature of cable suspended robots that cables can only pull the end effector, the cable tension values must be positive. In this paper, a method is used that cable tension values obtained positive for each initial condition and any desired path. Adaptive controller is designed such that unknown parameters of system is correctly estimated and system stability is guaranteed. Through several numerical simulations accuracy of kinematic, dynamic model and applied controller is shown. In order to demonstrate the effectiveness of adaptive control, the comparison between the adaptive control method and the method of feedback linearization is performed.