The invention provides a method for synthesizing for non-probability time-varying reliability of a link mechanism containing a hinge gap. Firstly, according to the rod length and initial position of the link mechanism and specific characteristics of the hinge gap, a mathematic expression of a mechanism motion error function is obtained in combination with a vector method; secondly, rod length and hinge uncertainty information is introduced into an interval process model for establishing mechanism motion errors, and the time-varying uncertainty characteristic quantity of a mechanism motion precision limit state function is quickly calculated; thirdly, based on the first crossing theory and the dispersed strategy, index definition and solution of crossing failure possibility in any micro cyclic loading increment segment are completed, and then a time-varying reliability model is constructed; finally, the non-probability time-varying reliability index of motion precision serves as a target, non-probability reliability of mechanism existence conditions serves as a constraint condition, and synthesis of the non-probability time-varying reliability of the link mechanism containing the hinge gap is completed. In the process of mechanism synthesis, synthetic effects of uncertainty on the mechanism in a motion period are reasonably represented, and the time-varying reliability of the mechanism can be effectively improved.