Multivariate time series classification (MTSC) has become an important data mining method that plays an significant role in many fields. However, most of related studies either focus on mining correlations in different dimensions or on extracting more features. This leads to models that lack a deep understanding of the underlying data structures and have a reduced ability to generalize to other datasets. To address this issue, an end-to-end enhanced transformer-improved spatiotemporal dynamic graph neural network (DynaTGNet) is proposed for MTSC. To learn the relationships among MTS from a global perspective, we firstly introduce convolution self-attention mechanism and design an enhanced transformer module to capture the correlations. A spatiotemporal dynamic graph neural network is further introduced to capture the hidden spatiotemporal dependencies and predict the labels of MTS. Also, the network is given a certain memory to capture the dynamic changes of MTS, where a dynamic graph constructor generates dynamically learnable parameters to build a dynamic graph for each moment. Extensive experiments conducted on 26 UEA benchmark datasets show that DynaTGNet exhibits impressive accuracy improvements over the state-of-the-art methods in MTSC tasks.