This paper presents a new method to accelerate tracing the boundaries of time-delay stability region in power systems.Using the periodical characteristics of the critical enginvalues of the critical points，a critical function is formulated by space mapping，and then solved in a finite interval by bisection method.By this way，the critical enginvalues of the critical points and their corresponding information can be derived and used to compute the critical time delay by the inverse mapping.The small disturbance based method is also proposed to determine the small signal stability region.Then the proposed methods are applied to time-delay space in larger scale，the computational speed and accuracy are verified on the classical3-machine9-bus test system.And it is found in further analysis of the results that the introduction of time delay can only leads to Hopf bifurcation rather than saddle node bifurcation for a given stable system.