Multivariate time series forecasting has long been a research hotspot because of its wide range of application scenarios. However, the dynamics and multiple patterns of spatiotemporal dependencies make this problem challenging. Most existing methods suffer from two major shortcomings: (1) They ignore the local context semantics when modeling temporal dependencies. (2) They lack the ability to capture the spatial dependencies of multiple patterns. To tackle such issues, we propose a novel Transformer-based model for multivariate time series forecasting, called the spatial–temporal convolutional Transformer network (STCTN). STCTN mainly consists of two novel attention mechanisms to respectively model temporal and spatial dependencies. Local-range convolutional attention mechanism is proposed in STCTN to simultaneously focus on both global and local context temporal dependencies at the sequence level, which addresses the first shortcoming. Group-range convolutional attention mechanism is designed to model multiple spatial dependency patterns at graph level, as well as reduce the computation and memory complexity, which addresses the second shortcoming. Continuous positional encoding is proposed to link the historical observations and predicted future values in positional encoding, which also improves the forecasting performance. Extensive experiments on six real-world datasets show that the proposed STCTN outperforms the start-of-the-art methods and is more robust to nonsmooth time series data.