This paper proposed a novel dynamic quantum secret sharing protocol in high-dimensional quantum system. Via transmitting the particles circularly and local unitary operations, the dealer and all agents can share the multi-particle entangled GHZ state in high-dimensional quantum system. The proposed protocol allows a dealer to share the predetermined dits without directly distributing any piece of shares to agents. To recover the secrets, dealer and all agents only need to perform the single-particle measurement operation and then implement the simple modular arithmetic operation according to their corresponding measurement results. Besides, in the proposed protocol, only a little fraction of entangled GHZ states are employed for eavesdropping check instead of lots of decoy (or detecting) particles used in previous protocols. Since the protocol is designed in the high-dimensional quantum system, it makes our protocol have higher resource capacity and better security in detecting the illegal eavesdropper than former protocols designed in two-dimensional quantum system. Security analyses indicate that the proposed protocol is immune to general attacks of intercept-and-resend, entangle-and-measure, collusion, and revoked a dishonest agent. Furthermore, the efficiency of proposed DQSS protocol in noise environment is deduced through quantum fidelity. The obtained results indicate that the efficiency of proposed protocol decreases with the increase in channel noise parameter and it has a quite different efficiency in four types of noise, i.e., dit-flip, d-phase-flip, amplitude-damping and depolarizing.