The imbalance and concept drift problems in data streams become more complex in multi-class environment, and extreme imbalance and variation in class ratio may also exist. To tackle the above problems, Hybrid Sampling and Dynamic Weighted-based classification method for Multi-class Imbalanced data stream (HSDW-MI) is proposed. The HSDW-MI algorithm deals with imbalance and concept drift problems through the hybrid sampling and dynamic weighting phases, respectively. In the hybrid sampling phase, adaptive spectral clustering is proposed to sample the data after clustering, which can maintain the original data distribution; then the sample safety factor is used to determine the samples to be sampled for each class; the safe samples are oversampled and the unsafe samples are under-sampled in each cluster. If the data stream is extremely imbalanced, the sample storage pool is used to extract samples with a high safety factor to add to the data stream. In the dynamic weighting phase, a dynamic weighting method based on the G-mean value is proposed. The G-mean values are used as the weights of each base classifier in the ensemble and the ensemble is dynamically updated during the processing of the data stream to accommodate the occurrence of concept drift. Experiments were conducted with LB, OAUE, ARF, BOLE, MUOB, MOOD, CALMID, and the proposed HSDW-MI on 10 multi-class synthetic data streams with different class ratios and concept drifts and 3 real multi-class imbalanced streams with unknown drifts, and the results show that the proposed HSDW-MI has better classification capabilities and performs more consistently compared to all other algorithms.