Heterogeneous graph neural networks (HGNNs) were proposed for representation learning on structural data with multiple types of nodes and edges. Researchers have developed metapath-based HGNNs to deal with the over-smoothing problem of relation-based HGNNs. However, existing metapath-based models suffer from either information loss or high computation costs. To address these problems, we design a new Metapath Context Convolution-based Heterogeneous Graph Neural Network (MECCH). Specifically, MECCH applies three novel components after feature preprocessing to extract comprehensive information from the input graph efficiently: (1) metapath context construction, (2) metapath context encoder, and (3) convolutional metapath fusion. Experiments on five real-world heterogeneous graph datasets for node classification and link prediction show that MECCH achieves superior prediction accuracy compared with state-of-the-art baselines with improved computational efficiency.