Understanding and predicting the Madden-Julian Oscillation (MJO) is fundamental for precipitation forecasting and disaster prevention. To date, long-term and accurate MJO prediction has remained a challenge for researchers. Conventional MJO prediction methods using Numerical Weather Prediction (NWP) are resource-intensive, time-consuming, and highly unstable (most NWP methods are sensitive to seasons, with better MJO forecast results in winter). While existing Artificial Neural Network (ANN) methods save resources and speed forecasting, their accuracy never reaches the 28 days predicted by the state-of-the-art NWP method, i.e., the operational forecasts from ECMWF, since neural networks cannot handle climate data effectively. In this paper, we present a Domain Knowledge Embedded Spatio-Temporal Network (DK-STN), a stable neural network model for accurate and efficient MJO forecasting. It combines the benefits of NWP and ANN methods and successfully improves the forecast accuracy of ANN methods while maintaining a high level of efficiency and stability. We begin with a spatial-temporal network (STN) and embed domain knowledge in it using two key methods: (i) applying a domain knowledge enhancement method and (ii) integrating a domain knowledge processing method into network training. We evaluated DK-STN with the 5th generation of ECMWF reanalysis (ERA5) data and compared it with ECMWF. Given 7 days of climate data as input, DK-STN can generate reliable forecasts for the following 28 days in 1-2 seconds, with an error of only 2-3 days in different seasons. DK-STN significantly exceeds ECMWF in that its forecast accuracy is equivalent to ECMWF's, while its efficiency and stability are significantly superior.