In this paper, a novel amplitude-phase modulation format, inverse-return-to-zero minimum shift keying (IRZ-MSK), is proposed. A scheme to realize the IRZ-MSK is introduced, and especially a method of demodulating the phase branch is presented. The influence of different duty cycles on the performance of the IRZ-MSK is discussed. Numerical simulations and analysis are performed, and the comparison between the 70% IRZ-MSK and the NRZ-MSK is made. The phase branches of 70% IRZ-MSK and the NRZ-MSK almost have the same dispersion tolerance, and the amplitude branch of 70% IRZ-MSK has a better dispersion tolerance than that of the NRZ-MSK when the residual dispersion is larger than 1.9ps/nm/km. For the nonlinear tolerance, the EOP of the IRZ-MSK phase branch and amplitude branch reduces 0.5dB and 3.8dB than those of the NRZ-MSK respectively, when the launch power is 4mW and dispersion is completely compensated. Meanwhile, the BER curves of the NRZ-MSK and IRZ-MSK are also made. The results show that, our proposed IRZ-MSK can not only improve the spectral efficiency, but also greatly mitigate the dispersion and nonlinear effects.