Mobile Crowdsourcing (MCS) has become an emerging paradigm evolved from crowdsourcing by employing advanced features of mobile devices such as smartphones to perform more complicated, especially spatial tasks. One of the key procedures in MCS is to collect answers from mobile users (workers), which may face several security issues. First, authentication is required to ensure that answers are from authorized workers. In addition, MCS tasks are usually location-dependent, so the collected answers could disclose workers' location privacy, which may discourage workers to participate in the tasks. Finally, the overhead occurred by authentication and privacy protection should be minimized since mobile devices are resource-constrained. Considering all the above concerns, in this paper, we propose a lightweight and privacy-preserving answer collection scheme for MCS. In the proposed scheme, we achieve anonymous authentication based on traceable ring signature, which provides authentication, anonymity, as well as traceability by enabling malicious workers tracing. In order to balance user location privacy and data availability, we propose a new concept named current location privacy, which means the location of the worker cannot be disclosed to anyone until a specified time. Since the leakage of current location will seriously threaten workers' personal safety, causing such as absence or presence disclosure attacks, it is necessary to pay attention to the current location privacy of workers in MCS. We encrypt the collected answers based on timed-release encryption, ensuring the secure transmission and high availability of data, as well as preserving the current location privacy of workers. Finally, we analyze the security and performance of the proposed scheme. The experimental results show that the computation costs of a worker depend on the number of ring signature members, which indicates the flexibility for a worker to choose an appropriate size of the group under considerations of privacy and efficiency.