By using a vectorial approach, the validity of paraxial approximation in second harmonic generation (SHG) microscopy under low numerical aperture (NA) is examined when the sample is a collagen fibril. Due to the larger value of dzzx and tensorial nature of SHG, the component Ez of the focused field may have strong effect on the radiation patte of SHG. Numerical results indicate that when the value of NA exceeds 0.3, the effect of Ez can not be neglected, which results in the invalidation of paraxial approximation in SHG microscopy despite the fact that SHG microscopy is still under low NA focusing.