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In this paper, a chaotic system with surface equilibrium and a hidden attractor was studied, and the dynamical behavior, synchronization scheme and circuit application of the system were analyzed. Firstly, the stability analysis and dynamic behavior of the system were carried out (the type of attractor, bifurcation, Poincaré section, Lyapunov exponents spectrum and complexity). Secondly, the finite-time synchronization observer was designed according to the finite-time stability theorem to achieve the synchronization of the finite-time master–slave systems, and the error system asymptotically approached zero. Finally, the existence and practicability of the original system were proven through the implementation of the circuit system, and through using an appropriate control circuit to realize the synchronization of chaotic master–slave systems.