Trapping forces of core-shell particles trapped by Laguerre-Gaussian beams (LGpl beams) are calculated using T-matrix method. The results show that both the maximum of axial and radial trapping efficiencies and trapping regions of optical tweezers increase with the numerical apertures of objective, while the axial and radial trapping efficiencies reduce with too big or too small numerical apertures of objective. The axial and radial trapping efficiencies of optical tweezers increase with the refractive indices of particles cladding, when the refractive indices of particles core are greater than the refractive indices of particles cladding. The axial and radial trapping efficiencies of optical tweezers decrease with the refractive indices of particles cladding, when the refractive indices of particles core are less than the refractive indices of particles cladding. The axial trapping efficiencies increase firstly and then decrease with the azimuthal model index (l) of the LGpl beams. The maximum of axial trapping efficiencies decrease and the curve is parallel to x-axis gradually with the increase of the radial model index (p) of the LGpl beams.