As a promising distributed computing paradigm, Federated Learning (FL) enables effective and secure knowledge sharing in mobile crowdsourcing. In FL, the incentive mechanism drives the model transaction between server and workers. However, traditional incentive mechanisms require complete information during interaction, which discloses the private attributes of workers and poses risks in terms of privacy. Moreover, the notorious data imbalance issue impacts the training utility of workers, which is more complex when it is coupled with the design of incentive. Based on the above issues, we propose a data-balanced and privacy-preserving incentive mechanism for FL based on Multi-Agent Deep Reinforcement Learning (MADRL). First, a Stackelberg game is established to measure the multi-dimensional contribution and provide the fair reward for workers. To shield the privacy of workers, we design a MADRL-based strategy optimization with incomplete information, which makes the system reach Nash Equilibrium (NE). Moreover, considering the data imbalance in FL, a Data Secondary Recruitment (DSR) scheme is proposed for cloud server to balance training data and maximize model utility. Finally, experiment analysis demonstrates our incentive mechanism has significant improvement on model performance and system utility compared with other methods under data imbalance settings.