Abstract: To narrow the signal spectrum of a random-polar and modified CP-EBPSK (MCP-EBPSK) modulation and eliminate the discrete components in spectral sideband, an asymmetry and random-polar very minimum amplitude phase modulation (ARP-VMAP) is proposed. This modulation is prone to circuit implementation and chip integration. The method of this modulation is a simplification and approximation of the waveform expressions of random-polar MCP-EBPSK modulation by eliminating its transcendental function, which makes the modulator easier to circuit implementation and higher in carrier frequencies. The simulation results show that even in the severe condition of the -74dB power spectral bandwidth, the ARP-VMAP modulation can remove the discrete component in power spectrum of the modulated signal, get higher spectrum efficiency and much better demodulation performance than random-polar MCP-EBPSK modulation. As a result the ARP-VMAP modulation can successfully make the utilization rate of the launch energy higher than before and has the advantage in energy conservation and environmental protection