The motif discovery of multi-dimensional time series datasets can reveal the underlying behavior of the data-generating mechanism and reflect the relationship between time series in different dimensions. The study of motif discovery is of important significance in environmental management, financial analysis, healthcare, and other fields. With the growth of various information acquisition devices, the number of multi-dimensional time series datasets is rapidly increasing. However, it is difficult to apply traditional multi-dimensional motif discovery methods to large-scale datasets. This paper proposes a novel method for motif discovery and analysis in large-scale multi-dimensional time series. It can effectively find multi-dimensional motifs and the correlation among the motifs. The experimental results show that the proposed method achieves better performance than the related arts on synthetic and real datasets. It is further validated on practical air quality data and provides theoretical support for real air pollution control in places such as Beijing.