Spatial Crowdsourcing (SC) has been adopted in various applications such as Gigwalk and Uber, where a platform takes location-based tasks (e.g., picking up passengers) from a requester and selects suitable workers to perform them. In most existing works, the platform selects workers based on the requester and worker information, which suffers from serious privacy issues. Some works have considered privacy issues, but they still suffer from either of two limitations: (i) Privacy of the requester and worker cannot be protected simultaneously; (ii) Third-party trusted entities are usually required. Motivated by this, we focus on protecting the privacy of both the requester and the worker without third-party entities while selecting workers. We use randomized response, a widely recognized and prevalent privacy model achieving Local Differential Privacy (LDP), to jointly protect the privacy of workers’ locations and charges based on the location-charge correlation. For the requester, we present a novel mechanism called randomized matrix multiplication to hide the real task locations. More importantly, we prove that the worker selection based on the protected information is non-submodular and NP-hard, which cannot be addressed in polynomial time. To this end, we present an approximate algorithm to solve the problem efficiently, of which the effectiveness is measured by the approximation ratio, i.e., the ratio of the optimal solution to the approximate solution. Finally, simulations based on real-world datasets illustrate that our worker selection outperforms the state-of-the-art method on both privacy protection and worker selection.