Multivariate time series forecasting has attracted wide attention in areas, such as system, traffic, and finance. The difficulty of the task lies in that traditional methods fail to capture complicated non-linear dependencies between time steps and between multiple time series. Recently, recurrent neural network and attention mechanism have been used to model periodic temporal patterns across multiple time steps. However, these models fit not well for time series with dynamic-period patterns or nonperiodic patterns. In this paper, we propose a dual self-attention network (DSANet) for highly efficient multivariate time series forecasting, especially for dynamic-period or nonperiodic series. DSANet completely dispenses with recurrence and utilizes two parallel convolutional components, called global temporal convolution and local temporal convolution, to capture complex mixtures of global and local temporal patterns. Moreover, DSANet employs a self-attention module to model dependencies between multiple series. To further improve the robustness, DSANet also integrates a traditional autoregressive linear model in parallel to the non-linear neural network. Experiments on real-world multivariate time series data show that the proposed model is effective and outperforms baselines.