The advancement and rising of information technology have promoted the flipped classroom in an effective way. It flips knowledge transfer and knowledge internalization from two levels of teaching structure and teaching process, reversing the traditional teaching knowledge transfer in class and knowledge deepening after class from time and space. Although the use of flipped classrooms in ideological and political theory courses is relatively uncommon in colleges and universities, realistic teaching and related study findings in some colleges and universities provide some reference value for the use of flipped classrooms in ideological and political theory courses. As a result, the short- and long-time memory network-based flipped classroom design algorithm for ideological and political courses in colleges and universities has a wide range of applications. A neural network prediction model based on a hybrid genetic algorithm is developed in this paper. The hybrid genetic algorithm is used in this model to determine the optimal dropout probability and the number of cells in the hidden layer of the neural network. The hybrid genetic algorithm will lengthen the memory neural network to predict the teaching quality of root mean square error between real value and predictive value as a fitness function, in the process of optimization, genetic algorithm convergence to the local optimal solution of the area.