In this study, a new sequential convex programming (SCP) method was developed to improve the efficiency of stress-based topology optimization. In the topology optimization, the number of design variables is much larger than the number of objective and constraint functions, therefore, an optimization is performed using a sequential approximate optimization (SAO) technique based on the dual method. In general, one point approximation using function and derivative values at present design point is mainly used for SAO. In case of stress-based topology design, however, optimization efficiency becomes poor due to nonlinearity of stress constraints. Therefore, in this study, a two point approximation was used to generate approximate function which uses an enhanced two-point diagonal quadratic approximation to generate highly accurate diagonal Hessian terms. The efficiency of the proposed method was validated by comparing with the the method of moving asymptotes(MMA), which is the generally used in the topology optimization.