Low-rank tensor learning has many applications in machine learning. A series of batch learning algorithms have achieved great successes. However, in many emerging applications, such as climate data analysis, we are confronted with largescale tensor streams, which pose significant challenges to existing solutions. In this paper, we propose an accelerated online low-rank tensor learning algorithm (ALTO) to solve the problem. At each iteration, we project the current tensor to a low-dimensional tensor, using the information of the previous low-rank tensor, in order to perform efficient tensor decomposition, and then recover the low-rank approximation of the current tensor. By randomly selecting additional subspaces, we successfully overcome the issue of local optima at an extremely low computational cost. We evaluate our method on two tasks in online multivariate spatio-temporal analysis: online forecasting and multi-model ensemble. Experiment results show that our method achieves comparable predictive accuracy with significant speed-up.