We developed a method to fabricate a periodic array of three-dimensional crescent-like holes (3DCLH) via an inverted hemispherical colloidal lithography. It is found that there exists an extraordinary optical transmission in this non-planar perforated periodic array of 3DCLH when the electric field of the incident light is perpendicular to the cross-line of the crescent-like hole. This extraordinary optical peak is insensitive with the incident angles and sensitive with the angle between the electric field of the incident light to the cross-line of the 3DCLH. Numerical simulation based on finite-difference time-domain method reveals that this peak is caused by an asymmetric localized surface plasmon resonance. This structure might be useful for the optical sensing and optical-integrated circuits.