The service volume of online customer service system is affected by many factors. In order to improve the prediction accuracy of service volume, an improved algorithm IDMPSADE is proposed on the basis of self-adaptive differential evolution algorithm DMPSADE with discrete mutation control parameters. By combining IDMPSADE with Long-Short Term Memory network (LSTM), an IDMPSADE-LSTM prediction model of service volume is established. IDMPSADE chooses the reverse guidance of the parent population whose child population’s performance on test functions is not as good as it, which can escape from the local optimum and improve the capability of searching the optimal solution within defined space. LSTM’s parameters, such as number of neurons, epochs, learning rate, and batch-size, are set by experience and have larger randomness, and IDMPSADE could be helpful to optimize these parameters. IDMPSADE-LSTM prediction model uses temperature and precipitation as influencing factors and combines with the temporal characteristics of service volume to predict the service volume. The experimental results show that the proposed IDMPSADE-LSTM prediction model is more accurate compared with general neural networks and SARIMA-SVM hybrid prediction model.