In order to improve the calculation speed of the dynamic security region, this paper, based on the SIME (Single Machine Equivalent) proposes a new method to calculate critical points in active power injection space. When a search direction is given, based on the characteristics of dynamic security domain, a non-linear map model is presented between n-dimensional space of active power injection and mechanical power of one-machine infinite-bus system. Experimental data suggest that when the SIME method is used to calculate the critical mechanical power of one-machine infinite-bus system, one-sided approximating method is of great rapidity. Considering this feature, Newton method is modified. The second order convergence rate can be obtained by using this modified method to solve the non-linear map model. Simulation on IEEE 10-generator 39-bus system shows that the calculation speed of the new method increases significantly when it is compared with the traditional method.