In view of the relaxation and ungrooving of the power rope of the antenna deployment mechanism in the process of antenna deployment and folding, the deployment mechanism of the high precision satellite umbrella antenna is taken an the research object. The working principle of the antenna deployment mechanism ia analyzed. The equation of motion of the deployment mechanism is obtained by analytical method. Combined with the structural parameters of the parts of the antenna deployment mechanism, the relaxation law of the power rope of the deployment mechanism is obtained. Taking the structural parameters of the deployment mechanism as the design variable and minimun relaxation of the power rope as the goal, the structure optimization model of the deployment mechanism is obtained. The structural parameters of the optimized deployment mechanism are obtained by simulated annealing algorithm. The relaxation of the power rope of the optimized deployment mechanism is reduced by 90% compared with that before optimization, and the optimization effect is remarkable.