As an emerging “human problem solving strategy”, crowdsourcing has attracted much attention where requesters want to employ reliable workers to complete specific tasks. Task assignment is an important branch of crowdsourcing. Most existing studies in crowdsourcing have not considered self-interested individuals’ strategy. To guarantee truthfulness, auction has been regarded as a promising method to charge the requesters for the tasks completed and reward the workers for performing the tasks. In this study, an online task assignment scenario is considered where each worker has a set of experienced skills, whereas a specific task is budget-constrained and requires one or more skills. In this scenario, the crowdsourcing task assignment was modeled as a reverse auction where the requesters are buyers and the workers are sellers. Three incentive mechanisms, namely, Truthful Mechanism for Crawdsourcing-Vickrey-Clarke-Grove (TMC-VCG), TMC-Simple Task (ST) for a simple task case, and TMC-Complex Task (CT) for a complex task case are proposed. Here, a simple task case means that the requester asks for a single skill, and a complex task case means that the requester asks for multiple skills. The related properties of each of the three mechanisms are determined theoretically. Moreover, the truthfulness is verified, and other performances are evaluated by extensive simulations.