Gray model is widely used in mid-long term electricity demand forecasting, but the model fits exponentially increasing data more precisely. Due to China's economic growth rate fluctuations, the increase in electricity consumption is slowing down, and electricity varies stochastically. So it is necessary to propose a new model to reflect the new situation. To solve the problem of the poor anti-interference ability of grey model, this paper proposes a model with Fourier series and Markov theory residual error correction based on grey model. This model applies Fourier series method to optimize electricity changing rate, and Markov chain method to embed the random property in gray forecasting model for doubly correcting the residual error, which can improve the adaptability and flexibility. The proposed model is verified by actual load data, and it indeed improves the forecasting accuracy.