Large-scale wind power access reduces the inertia level of a power system and increases the risk of transient power angle instability. Carrying out online warning of transient power angle stability before faults in power systems with wind power is essential to ensure their safety and stability. An online early warning method for the transient power angle stability of power systems with wind power based on critical inertia and anticipated faults is proposed. First, a theoretical analysis is used to obtain the inference that the power recovery process of a wind farm cannot be neglected for a short period of time after fault clearance, and an equivalent external characteristic model is established. A mathematical model is constructed based on the extended equal area rule to take into account the multi-stage characteristics of wind farms. Second, the critical equivalent inertia of the transient power angle stability of power systems with wind power is defined, and a practical solution is proposed by means of uniformly accelerated segmental equivalence. A transient critical-inertia index is then proposed to quantify the stability margin analysis and give a risk rating. Finally, the validity and applicability of the proposed method is verified by simulation using a four-machine two-area system with wind power access and an IEEE39 system as examples.