In this Letter, we theoretically propose an all-dielectric quasi-three-dimensional subwavelength structure constructed by a dielectric metasurface cascaded with a multilayer photonic crystal (PC) to achieve a high-performance asymmetric optical transmission (AOT). The desired optical control of the AOT is realized by combining the predetermined anomalous beam steering of a phase gradient metasurface with a unique bandgap as well as transmission characteristics of the multilayered stacked PC. The simulated results demonstrate that the proposed AOT device operating at the center wavelength of 633 nm with a circularly polarized state exhibits a high transmission of up to 62.4% with a contrast ratio exceeding 606. The excellent performance of AOT is achieved by making disassembled transverse magnetic and transverse electric polarized light under the same deflection angle concurrently match with respective high-efficient transmission bands in the multilayer PC. Furthermore, dependence of the performance of the proposed device on structural dimensions is also explored. Fortunately, the designed AOT structure is applicable to any linearly polarized light but is accompanied by double diffraction channels as compared to the circularly polarized light case. Owing to its planar configuration, passive operation, and compelling performance under various polarization states, the proposed strategy for achieving AOT paves a new road for realizing high-performance optical metadevices in compact optical systems.