We introduce a novel phase-field model designed for ternary Cahn-Hilliard (CH) dynamics, incorporating contact angle boundary conditions within complex domains. In this model, we utilize a fixed phase field variable to accurately represent intricate domains within the ternary CH system. Simultaneously, the remaining two phase field variables are employed to simulate CH dynamics effectively. The contact angle term is derived from Young’s equality and the hyperbolic tangent profile of the equilibrium interface. To ensure compliance with the hyperbolic tangent property at the interface, a fidelity term is incorporated into the original CH model. This addition reduces mass loss for each phase and improves the accuracy of the contact angle effect. Moreover, we implement a finite difference scheme along with a nonlinear multigrid method to solve the corrected ternary CH model. A series of numerical experiments is conducted in both two- and three-dimensional spaces to demonstrate the efficiency and robustness of the proposed model.