Given the influence of the weak inertia and zero inertia characteristics of grid-connected new energy on power system frequency stability, a new energy power system critical inertia estimation method that takes into account frequency stability constraints is proposed. First, this paper establishes a mathematical model of the system frequency dynamic response, and solves the time-domain expression of the inertia center frequency. Then, based on the frequency response model, the relationship between the system inertia and the related frequency stability index is established and analyzed, and then the frequency change rate and the frequency maximum deviation constraints are considered in order to estimate the theoretical and calculated values of the system critical inertia. Finally, based on the critical inertia, a power system frequency stability index is proposed to evaluate that stability after a power disturbance, and is combined with the actual operating inertia of the power system to obtain a reference value of the new energy virtual inertia. In DIgSILENT PowerFactory, an improved IEEE 10-machine 39-node New England system and a regional power grid simulation example are used to simulate and verify the proposed calculation method. This work is supported by the National Natural Science Foundation of China (No. 51977128) and the Shanghai Science and Technology Commission-funded Projects (No. 17020500800).