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Aiming at the design problem of multi-missile cooperative guidance law for attacking high-speed targets, a design method of multi-missile cooperative guidance law based on the working characteristics of pulse engine is proposed. Firstly, the relative motion equation of missile and target is solved. Secondly, the finite-time consistency theory is used to design the cooperative guidance law in the line-of-sight direction, and the sliding mode variable structure control theory is used to design the line-of-sight angle constrained guidance law in the line-of-sight normal direction. Then, for the overload command in the line-of-sight direction, considering the working characteristics of the pulse engine, the continuous guidance command in the line-of-sight system is transformed into discrete guidance command, and then the multi-missile cooperative guidance is realized. Finally, the feasibility and effectiveness of the designed multi-missile cooperative guidance law are verified by numerical simulation.