An advanced Actuator Surface Method (ASM) coupled with Computational Fluid Dynamics (CFD) is developed and applied to the complex unsteady aerodynamic simulation of helicopter. By introducing an improved three-dimensional anisotropic Gaussian kernel, this method effectively addresses the severe aerodynamic load fluctuations commonly associated with traditional Virtual Blade Method (VBM) due to turbulent flow around blade elements. To manage the issues of regional shape and grid cell quantity variations caused by virtual blade sweeping, a universal hybrid grid generation strategy is established without body-fitted and disk interpolation grids, which enhances the computational stability at both blade elements and blade edges. Aerodynamic numerical simulations of helicopter are performed using this method, focusing on rotor/fuselage interaction dominated by rotor wake motion and fuselage blockage effects, Blade-Vortex Interaction(BVI) induced by tip vortices, and maneuvering flights involving collective pitch ramp increases. The results indicate that the advanced ASM demonstrates reliability and robustness in the simulation of complex unsteady flow fields around helicopter. Under similar computational accuracy, the advanced ASM improves computational efficiency by nearly 40 times compared to the overset-grid-based full Blade-Resolved (B-R) method, and by 6 times compared to the VBM. It shows significant advantages when applied to complex full-aircraft interaction and maneuvering flight conditions that require substantial computational resources.