In crowdsourcing markets, there are two different type jobs, i.e. homogeneous jobs and heterogeneous jobs, which need to be allocated to workers. Incentive mechanisms are essential to attract extensive user participating for achieving good service quality, especially under a given budget constraint condition. To this end, recently, Singer et al. propose a novel class of auction mechanisms for determining near-optimal prices of tasks for crowdsourcing markets constrained by the given budget. Their mechanisms are very useful to motivate extensive user to truthfully participate in crowdsourcing markets. Although they are so important, there still exist many security and privacy challenges in real-life environments. In this paper, we present a general privacy-preserving verifiable incentive mechanism for crowdsourcing markets with the budget constraint, not only to exploit how to protect the bids and assignments privacy, and the chosen winners privacy in crowdsourcing markets with homogeneous jobs and heterogeneous jobs and identity privacy from users, but also to make the verifiable payment between the platform and users for crowdsourcing applications. Results show that our general privacy-preserving verifiable incentive mechanisms achieve the same results as the generic one without privacy preservation.