Personalized venues recommendation is essential to help people find attractive venue to visit as growth of location-based social networks. Existing approaches never distinguish user individual interests from her social preferences, which leads to a bottleneck of modeling user check-in behaviors accurately. In this paper, we find the differences between user interests and her social preferences clearly and investigate the time law of user check-in behaviors in depth. Consequently, we propose a social-period-aware topic model (SPATM) to learn the influence weights of both user interests and her social preferences on making-decision for each check-in time automatically. Especially, we model latent topic by leveraging smaller size of dynamic activities instead of static categories, which can alleviate the data sparsity problem by using more co-occurrent activities information. Moreover, our approach can automatically judge whether a user's social preference is periodic or aperiodic and learn the periodicity of periodic one. Furthermore, the Alias Sampling based training approach is introduced to improve sampling efficiency. The results demonstrate our proposed model is effective and outperforms the state-of-the-art approaches in terms of effectiveness and efficiency. Besides, SPATM can learn semantically coherent latent topics and geographically dispersed latent social topics which are useful to explain recommendation.