We present the first use of a waveform-dependent absorbing metasurface for high-power pulsed surface currents. The new type of nonlinear metasurface, composed of circuit elements including diodes, is capable of storing high power pulse energy to dissipate it between pulses, while allowing propagation of small signals. Interestingly, the absorbing performance varies for high power pulses but not for high power continuous waves (CWs), since the capacitors used are fully charged up. Thus, the waveform dependence enables us to distinguish various signal types (i.e. CW or pulse) even at the same frequency, which potentially creates new kinds of microwave technologies and applications.