The sequential pattern in the human movement is one of the most important aspects for location recommendations in geosocial networks. Existing location recommenders have to access users' raw check-in data to mine their sequential patterns that raises serious location privacy breaches. In this paper, we propose a new Privacy-preserving LOcation REcommendation framework (PLORE) to address this privacy challenge. First, we employ the nnth-order additive Markov chain to exploit users' sequential patterns for location recommendations. Further, we contrive the probabilistic differential privacy mechanism to reach a good trade-off between high recommendation accuracy and strict location privacy protection. Finally, we conduct extensive experiments to evaluate the performance of PLORE using three large-scale real-world data sets. Extensive experimental results show that PLORE provides efficient and highly accurate location recommendations, and guarantees strict privacy protection for user check-in data in geosocial networks.