Steam assisted gravity drainage (SAGD) is an effective technology to develop heavy oil reservoir, yet with large energy consumption and intense greenhouse emission. Therefore, it is important to predict the steam chamber development process and production performance of SAGD process. In early research, a lot of research has been conducted on the prediction of SAGD productivity analytically under some simplification. According to tens of numerical reservoir simulation results with STARS, we find that oil production rate is greatly linked to the steam injection rate. As to our knowledge, few studies have been published to build a relationship between them. In this paper, we propose a new analytical model to predict steam chamber development process and SAGD production performance under constant steam injection rate simultaneously. On the basis of previous numerical and experimental research, we assume that the steam chamber shape is a combination of two symmetrical parabolas or an inverted triangle. The oil production rate is expressed by the steam chamber expansion rate as a function of reservoir properties and injection parameters. An energy balance equation is employed to connect the steam expansion rate and heat loss rate to surrounding formation. Comparisons have been made between the new model results and STARS results for a specific super-heavy oil reservoir case in Canada and similarity is observed with the parabola-shape assumption. With the new proposed model, production performance, such as oil production rate, water cut and steam oil ratio, can be predicted.