Mobile crowdsensing (MCS) has become a popular and promising paradigm in various sensing applications in urban scenarios. In recent years, some social network-based MCS systems, which utilizing the social relationship to recruit participants or perform sensing tasks, have been proposed. However, none of them have taken into consideration both the time-sensitive and Sybil-proofness, which are the two key problems for the MCS systems in the social network context. We present two social network-based MCS system models, and formulize the Sybil attack models for each model. We design two incentive mechanisms based on reverse auction, time-sensitive and sybil-proof incentive mechanism in multi-bid model (TSSP-M), and time-sensitive and sybil-proof incentive mechanism in single-bid model (TSSP-S), for each of two system models. Through both rigorous theoretical analyses and extensive simulations, we demonstrate that TSSP-M satisfies the desirable properties of computational efficiency, individual rationality, truthfulness, time-sensitive, Sybil-proofness, and optimization; TSSP-S achieves individual rationality, truthfulness, time-sensitive, and Sybil-proofness.