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Coexistence of cooperation and defection is a common phenomenon in nature. The topic of why cooperation occurs among selfish individuals has attracted much attention in recent years. Generally, in the snowdrift game, when a defector exploits a cooperator, the defector would get the maximum benefit without paying any cost. However, the elapse of time is also a kind of loss. Even if the defector chooses to stay in the car waiting for cooperator to shovel snow, the defector also has to bear a loss of time. Under such circumstances, the time cost also should be considered in the total cost of shovelling snow. We focus on how time cost impacts the evolution of cooperation in the snowdrift game. More importantly, the experiments were implemented on hyperbolic networks which are closer to real world networks. Simulated results show that the larger proportion of time cost is, the more cooperation could be promoted.