Crowdsensing has become increasingly popular due to its ability to collect a massive amount of real-time data with the help of many individual smartphone users. A crowdsensing platform can utilize the collected data to extract effective information and provide services to service requesters. Due to the rationality of smartphone users, designing an incentive mechanism to compensate the participants for their resources consumption is critical in attracting more participation. Offline incentive mechanism design has been widely studied in various crowdsensing applications, whereas the online scenario, is much more challenging due to the unavailability of future information when the platform has to make user selection decisions. In this paper, we investigate the problem of online crowdsensing by considering a critical property that the values of users' contributions decrease as time goes by. The time- discounting property is common in inter-temporal choice scenarios but has not been carefully addressed in mechanism design perspective. To handle this problem, we propose a new method to select users based on a time-related threshold, and present a strategyproof framework where participants prefer to submit their true types, instead of manipulating the market by misreporting their private information. We prove that our mechanism can achieve computational efficiency, budget feasibility, strategy-proofness, and a constant competitive ratio. By comparing our mechanism with two heuristic benchmarks, we show that our design achieves great performance in terms of the total obtained value.