With the rapid development of mobile smart devices, mobile crowdsensing has become an attractive paradigm for sensor data collection. In a mobile crowdsensing system, the platform can publish a set of tasks and then recruit suitable mobile users to accomplish these tasks. In this paper, we study the budget-constrained task assignment problem for mobile crowdsensing. We assume users can choose to take different transportations for task execution, and different choices have different task coverages, travel expenses, and travel time. We model the crowdsensing system and formulate the budget-constrained task assignment problem under study. We prove this problem is NP-hard. To address this problem, we propose a Value/Reward Maximum First heuristic algorithm (VRMF). We present the detailed algorithm design and deduce its computational complexity. Simulation results validate the effectiveness of our proposed algorithm.