The authors take the quality of sensing data into consideration and design a reputation-aware incentive mechanism (RAIM) with the properties of truthfulness and individual rationality while maximising the weighted social welfare of the whole system. In addition, in order to reduce the computational complexity of RAIM and improve the system feasibility, the authors propose a heuristic algorithm RAIM-H, with the computational complexity of O(n(2)). Simulation results show the nice performance of the proposed mechanisms RAIM and RAIM-H in terms of the weighted social welfare and the average reputation. Specifically, RAIM can improve the weighted social welfare by 8.65 and 48.16% compared with trustworthy sensing for crowd management (TSCM) and random selection, respectively, with the number of smartphone users n = 16. Meanwhile, RAIM-H approaches to the maximum very well and can improve the weighted social welfare by 6.15% and 75% compared with TSCM and random selection, respectively, with the number of smartphone users n = 100.