Multivariate time series (MTS) prediction has been widely applied in a diverse range of fields including electricity, economics, finance, and traffic. Many studies have successfully constructed spatial and temporal convolution modules called spatio-temporal block (ST-block) for multivariate time series prediction. However, existing methods need to manually design the architecture topology based on ST-blocks, which is time-consuming and requires extensive expert experience. In this paper, we propose a Spatio-Temporal based Architecture Topology Search (STATS) method for multivariate time series prediction, which can automatically design the ST-block for multivariate time series prediction. In the STATS, we construct static and dynamic graphs topologically to integrate both static and dynamic information to obtain more expressive ST-graphs for the prediction task. Then, STATS explores the architecture topology with the differentiable search algorithm based on ST-blocks automatically. Extensive experiments on four commonly used multivariate time series prediction benchmark datasets demonstrate that our proposed method STATS can outperform the state-of-the-art baseline models.