We propose a continuous-variable quantum secret sharing scheme based on multi-ring discrete modulation, which we called MR-CVQSS. In this scheme, phase shift keying (PSK)-modulated coherent states are allowed to be further discretely modulated with different amplitudes, so that these modulated coherent states can be scattered on different amplitude rings in phase space. The advantage for this multi-ring structure is that the error probability of quantum detector for discriminating discretely-modulated coherent states (DMCSs) is more lower than that of original single-ring discretely modulated CVQSS, which is beneficial for improving the performance of whole CVQSS system. We derive the security bound for MR-CVQSS against both eavesdroppers and dishonest users, and the numerical simulation shows that the performance of MR-CVQSS in terms of both maximal transmission distance and maximal available number of users can be largely improved. Moreover, security analysis shows that the modulation variance of MR-CVQSS does not need to be very small, thereby improving the signal-to-noise ratio (SNR) of whole CVQSS system.