The paper presents the injection strategy of steam and nitrogen for one kind of non-condensable gases on SAGP (Steam And Gas Push) process in the presence of top water-bearing formation in heavy oil reservoir, which optimizes the energetic value using ANN (Artificial Neural Network). Top water thief zone is problematic to cause the water influx and the heat loss, and thereby reduces significantly the bitumen production efficiency. The valid amount of both steam and nitrogen is essential in order to accomplish the minimum energetic value and the production efficiency. The authors verify the prediction accuracy of the developed ANN by showing an intensive correlation with the time-consuming reservoir simulations. The optimal scenario results the increment of bitumen recovery up to around 16.1% and the decrement of objective function up to 13.72% compared to the SAGP with constant injection strategy. Before the chamber reaching the top water-bearing formation, nitrogen concentration maintains low level for chamber enlargement while both high pressure and nitrogen concentration are used to block the water influx into the heated zone after contacting the thief zone. In the period of late production, it reduced the injection pressure to enhance the thermal efficiency.