Art is a very practical activity, especially music art. Quality music education at colleges and universities is vital for the ideological and moral schooling of students. Owing to the rapid expansion of music education at graduate level, the building of therapeutic evaluation of music instruction is critical. In fact, most of the music instruction in colleges and universities has not built a scientific and appropriate evaluation system based on the actual teaching quality of the classroom. This work combines the emerging neural network (NN) technology with standard method of music teaching evaluation and proposes a novel method—Music Teaching Quality Evaluation Network (MTQEN). To effectively improve performance of the model, the method uses a one-dimensional convolutional neural network (1D-CNN) being optimized from three aspects: expanding the receptive field, reducing training parameters, and enhancing operationality. Instead of the traditional convolution layer, the dilated convolution layer is utilized to increase scope of local receptive field and to improve the feature extraction efficacy. To improve training rate and to eliminate dependency on batch size, the filter response normalization (FRN) is used. Moreover, global pooling is used to reduce the requisite training parameters and to improve the training efficiency. Results of the evaluation show that performance of MTQEN in term accuracy (95.6%) and recall (93.3%) is better than the other contemporary models. The method proposed has great significance in pedagogy of music and arts, whereas the network designed may be enhanced to effectively evaluate teaching in related domains as well.