Second-harmonic generation (SHG) through a proposed thin gold film with a periodic array of subwavelength nanoholes is numerically investigated. By using a recently developed microscopic classical theory and a full-vectorial three-dimensional finite-difference time-domain method, we demonstrate that the mirror symmetry of nanoholes in one direction restricts the polarization state of second-harmonic emission in the same direction. Numerical results show that the second-order nonlinear susceptibility $\chi ^{\left(2\right)}{}_{yyy}$ dominates in the process of SHG when the nanoholes possess mirror symmetry in the x-axis direction. It is also found that the surface plasmon resonance can result in the enhancement of SHG from metallic nanoholes.