The unidirectional asymmetry transmission is demonstrated based on quasi-accidental bound states in the continuum by a one-dimensional chiral photonic crystal slab (CPhCs) composed of tilted silicon nano-pillars. The chirality breaks symmetries on the far field polarization and radiation Q-factor between the upward and downward radiation channels. Accordingly, the CPhCs only supports the unidirectional maximal asymmetry transmission at fixed incident and conical angles. The numerical simulation indicates that the CPhCs obtains a circular dichroism of 0.99 and Q-factor of 753.7 at λ = 1.565 μm. In addition, the handedness of polarization is also effectively converted between the incidence and transmission, and the handedness depends on the incident direction and conical angle. Our scheme provides a feasible route for applications in manipulating polarization and chiral sensing.