Predictive spatio-temporal analytics aims to analyze and model the data with both spatial and temporal attributes for future forecasting. Among various models proposed for predictive spatio-temporal analytics, the recurrent neural network (RNN) has been widely adopted. However, the training of RNN models becomes slow when the number of spatial locations is large. Moreover, the structure of RNN is unable to dynamically adapt to incorporate new covariates or to predict the target variables with varying spatial dimensions. In this paper, we propose a novel method, named Mesoscale Anisotropically-Connected Learning (MACL), to address the aforementioned limitations in RNN. For efficient training, we group the dataset into clusters (which refers to the mesoscale) along the spatial dimension according to the spatial adjacency and develop individual prediction module for each cluster. Then we design an anisotropic information exchange mechanism (i.e., the information exchange is not symmetric), to allow the prediction modules leveraging state information from nearby clusters for enhancing the prediction accuracy. Furthermore, for timely adaptation, we develop a local updating strategy for adapting the learning model to incorporate new covariates and the target variables with varying spatial dimensions. Experimental results on a real-world prediction task demonstrate that our method can be trained faster and more accurate than existing methods. Moreover, our method is flexible to incorporate new covariates and target variables of varying spatial dimensions, without sacrificing the prediction accuracy.