Leighton Chajnantor Telescope (LCT) will be moved from the summit of Maunakea, Hawaii to Chajnantor Plateau, Chile and be refurbished there. Strong wind disturbance at the new site will bring great challenges to the servo control of LCT. It is necessary and important to develop a simulation platform that behaves as close as possible to the real telescope for testing the performance of the designed servo controller. In this paper, a collaborative simulation platform of LCT based on Adams and Matlab/Simulink is constructed. On this platform, the mechanical structure model of LCT can be integrated with its control system model such that a collaborative simulation of the mechanical structure and the control system of LCT can be conducted. The mechanical structure model of LCT, which contains both rigid body models (i.e., the mount) and flexible body models (i.e., the primary reflector), is developed by using Adams. The servo system model and the wind disturbance model are constructed by using Matlab/Simulink. By conducting collaborative simulation, the performances of the servo controller based on the rigid body model and the rigid-flexible coupling model of LCT are compared. The comparison shows that the controller designed based on the rigid body model does not perform well when it is employed to control the rigid-flexible coupling model of LCT. However, by readjusting parameters of the servo controller, its performance can be further improved when applied to the rigid-flexible coupling model. Therefore, an LCT model of integrated mechanical structure and control systems is very helpful for analyzing its performance more accurately and designing a better servo controller.