Geospatial data provides a lot of benefits for personalized services. However, since the geospatial data contains sensitive information about personal activities, collecting the raw data has a potential risk of leaking private information from the collectors. Recently, local differential privacy (LDP), which protects the privacy of users without trusting the collector, has been adopted to preserve privacy in many real applications. In this paper, we investigate the problem of collecting the locations of individual users under LDP, and propose a perturbation mechanism designed carefully to minimize the expected error of perturbed locations according to the privacy budget and the data domain. The frequency distribution of perturbed locations inevitably has a large error. To tackle the problem, we also propose a postprocessing algorithm to estimate the original frequency distribution of collected data by using convex optimization. By experiments with various real datasets, we show the effectiveness of the proposed algorithms.