Effective incentive mechanisms are invaluable in crowdsensing to stimulate the enthusiasm of strategic users. However, existing work focusing on multi-task allocation with the objective of purely maximizing the social utility may result in the problem of unbalanced allocation, which may damage the social fairness. This motivates us to introduce proportional fairness into the design of a novel fairness-aware incentive mechanism for the first time. Specifically, we first model the interaction of multi-task allocation in crowdsensing as a multi-requester multi-worker Stackelberg game, and then transform the fairness-aware multi-task allocation problem into a fairness-aware incentive mechanism design problem. Next, we prove that there is a unique Stackelberg equilibrium, and also show that it can be efficiently derived through cautiously proposed algorithms. Since the existing equilibrium may not be optimal, we further design a secondary allocation rule to maximize both social utility and system performance, while achieving proportional fairness at a minimum cost. Finally, extensive experiments using both synthetic and real-world datasets demonstrate the superiority of our proposed mechanism compared to the state of the arts.