A dynamic collapse criterion for elastic–plastic structures under near-fault ground motions is derived analytically by approximately transforming near-fault ground motions into double impulse and using an energy balance law. A negative post-yield stiffness is introduced to treat the P-delta effect in the single-degree-of-freedom (SDOF) model. The principal part of fling-step near-fault ground motions is modeled by a one-cycle sine wave and then a double impulse. The double impulse enables the efficient use of the energy approach in the derivation of compact expressions of complicated elastic–plastic responses of structures with the negative post-yield stiffness. In contrast to the previous work (Kojima and Takewaki, 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse. It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations. It is shown that discussions on several patterns of dynamic collapse behaviors introduced in the previous critical case are useful for deriving a boundary between the collapse and the non-collapse in the plane of the input velocity and the input frequency. The most important point to be remarked is that the critical state (Kojima and Takewaki, 2016b) corresponding to the non-linear resonance does not necessarily provide the minimum input velocity level with respect to arbitrary impulse timing. The validity of the proposed dynamic collapse criterion is examined by the numerical response analysis for structures under double impulses with collapse or non-collapse parameters.