Oil sand reservoirs play an important role in the economy of Canada due to their significant recoverable reserves. Due to the high viscosity of the oil in these reservoirs, conventional methods cannot be used for production. The steam-assisted gravity drainage (SAGD) method is an efficient way of producing oil from these reservoirs. Predicting oil production and steam injection rates is required for planning and managing a SAGD operation. This can be done by simulating the fluid flow with flow simulation codes, but this is very time consuming. The run time for a 3D heterogeneous model with one well pair can exceed 2 days. In this paper, a SAGD approximate simulator for predicting SAGD performance with 3D heterogeneous models of geologic properties is developed. This approximate simulator can handle different types of operating strategies. The approach is an approximate solution using a semi analytical model based on relevant theories including Butler's SAGD theory. The approximate simulator or proxy is much faster than the full simulator and it gives accurate estimated oil production and steam injection rates at different time steps. Theoretical and numerical research has been undertaken to develop the proxy, implement it in fast code, demonstrate the accuracy of prediction and apply to realistic examples. This proxy is used for other applications such as transferring uncertainty for reservoir realizations and well trajectory optimization.