Based on vectorial diffraction theory, an analytical integral representation to calculate the field gradient of focused electromagnetic fields is derived by use of the differential recursion formula of the Bessel functions with different order. Within the phenomenological model for second harmonic generation (SHG) of centrosymmetric material, second harmonic (SH) generation of single centrosymmetric spherical particle excited by a focused beam is investigated. With increasing numerical aperture, the SH radiation distributions of the surface and bulk responses are compared and discussed in term of the properties of the intensity and gradient distributions of the focused field. The results indicate that the influence of the variation of the focused field on the bulk response is more remarkable.