In recent years, the social economy has achieved remarkable development, and the income of residents has increased substantially. With the increasing income, residents begin to pursue a high quality of life, and the ways of entertainment also begin to become diversified. In this context, leisure sports have gradually come into the public’s view, and more and more people have started to participate in leisure sports. Aerobic gymnastics, as a popular form of fitness, is an important carrier to carry out national fitness sports and promote national health, and the development of national fitness sports cannot be carried out without scientific and effective aerobic gymnastics teaching, training, and guidance. At the present stage, the traditional aerobics teaching content and teaching methods of leisure sports majors are difficult to meet the needs of students learning. Therefore, the hybrid teaching system of aerobics classes based on cloud computing and neural networks is proposed, which combines the advantages of a network teaching and traditional teaching to comprehensively and effectively improve the efficiency and quality of aerobics teaching and improve the classroom teaching effect. At the same time, it promotes leisure sports students to systematically master the basic theoretical knowledge, skills, and methods, improve the comprehensive ability of independent learning and inquiry learning, have the ability of leisure sports program guidance and aerobics teaching organization, enhance their employability, and cultivate “multidiscipline” students who can adapt to the needs of the times and engage in technical guidance of aerobics and participate in leisure sports market services in leisure fitness clubs, industry associations, and educational institutions. This course aims to cultivate “multidiscipline” applied talents who can work in leisure and fitness clubs, industry associations, and educational institutions.