Cost of time passing plays an important role when investigate the collective behaviour in real world. Each rational individual can get a more reasonable strategy by comprehensively considering the time-cost. Motivated by the fact, we here propose a mechanism with individual time-cost heterogeneity whose core lies in three aspects: 1. Each individual is given a time-cost parameter that takes into account the effect of time-cost on benefits when they interact with their neighbors. 2. The time-cost is divided into a fixed time-cost that maintains a fixed value and a unfixed time-cost where each individual time-cost is different for each round. 3. Four different update methods are used to study evolution cooperating with time-cost on the rule lattice. Simulation results show that the proposed mechanism effectively promotes cooperation in the snowdrift game. Moreover, high time-cost are more conducive to higher levels of cooperation. Within the same range of time-cost, fixed time-cost promote cooperation better than unfixed time-cost. And among the four update methods, the asynchronous update method is better than the synchronous update method, and the results of the asynchronous update method are similar but the process is different.