Scattering of the focused Laguerre-Gaussian beams by a spherical particle is performed. According to the generalized Mie theory, the scattering coefficient expressions are gained. From the numerical simulations of the electric field distribution and scattering intensity of the focused Laguerre-Gaussian beams, the scattering intensities are discussed for different scattering angles, radii of spherical particles and topology changes, and the oscillatory behavior of the scattered intensity distribution is explained by the scattering coefficients. The results show that in the focused Laguerre-Gaussian beams, the backscattering intensity increases with the particle radius; and the particle radius when the scattering intensity begins to increase is related to the topological charge. Comparing with the Gaussian beams, we can see that the focuced Laguerre-Gaussian beams have different the scattering characteristics, so they have potential value for particle size measurement, optical communication, atmospheric backscattering detection, etc.