Mobile crowdsensing (MCS) is a new sensing framework that empowers normal mobile devices to participate in sensing tasks. The key challenge that degrades the performance of MCS is selfish mobile users who conserve the resources (e.g., CPU, battery and bandwidth) of their devices. Thus, we introduce energy harvesting (EH) as rewards into MCS and thus provide more possibilities to improve the quality of service (QoS) of the system. In this paper, we propose a game theoretic approach for achieving sustainable and higher-quality sensing task execution in MCS. The proposed solution is implemented as a two-stage game. The first stage of the game is the system reward game, in which the system is the leader, who allocates the task and reward, and the mobile devices are the followers who execute the tasks. The second stage of the game is called the participant decision-making game, in which we consider both the network channel condition and participant’s abilities. We analyse the features of the second stage of the game and show that the game admits a Nash Equilibrium (NE). Based on the NE of the second stage of the game, the system can admit a Stackelberg Equilibrium, at which the utility is maximized. Simulation results demonstrate that the proposed mechanism can achieve better QoS and prolong the system lifetime while also providing a proper incentive mechanism for MCS.