College is the main place to carry out music teaching, and it is important to assess the music teaching ability in college effectively. Based on this, this paper firstly analyzes the necessity of music teaching ability assessment and briefly summarizes the application of neural network and deep learning technology in music teaching ability assessment and secondly designs an assessment model based on compensated fuzzy neural network algorithm and analyzes the accuracy of the model, finds out the causes of forming abnormal output by analysing the general dimensional conditions of the algorithm of the model, and proposes corresponding correction. Finally, the reliability and feasibility of the music teaching ability assessment model were experimentally verified by combining with teaching practice. The research results confirm the feasibility of the compensated fuzzy neural network algorithm in music teaching ability assessment, which has important reference significance for improving the quality of music teaching in colleges and universities.