Music classification has been inspired by the remarkable success of deep learning. To enhance efficiency and ensure high performance at the same time, a hybrid architecture that combines deep learning and Broad Learning (BL) is proposed for music classification tasks. At the feature extraction stage, the Random CNN (RCNN) is adopted to analyze the Mel-spectrogram of the input music sound. Compared with conventional CNN, RCNN has more flexible structure to adapt to the variance contained in different types of music. At the prediction stage, the BL technique is introduced to enhance the prediction accuracy and reduce the training time as well. Experimental results on three benchmark datasets (GTZAN, Ballroom, and Emotion) demonstrate that: i) The proposed scheme achieves higher classification accuracy than the deep learning based one, which combines CNN and LSTM, on all three benchmark datasets. ii) Both RCNN and BL contribute to the performance improvement of the proposed scheme. iii) The introduction of BL also helps to enhance the prediction efficiency of the proposed scheme.