By using the Richards-Wolf vector diffraction theory,the focusing proper ties of higher-order Laguerre-Gaussian laser beams through a high numerical aperture with a diffract ive optical element (DOE) are investigated in this paper.The phase of the incoming higher-order Laguerre-Ga ussian laser is spatially modulated by a diffractive optical element (DOE).Numerical calculations are performed to com pare the influence of parameters on the tight focusing properties.The intensity distribution of higher-order La guerre-Gaussian laser after being focused by a high numerical aperture with a DOE is simulated.It is shown that a three-dimensional optical chain along optical axis can be obtained near the focus by spatially modulating the ph ase of incoming beam,and the particles whose refractive index is lower than that of the ambient could simulta neously be trapped by use of focused higher-order Laguerre-Gaussian laser beams.The effects of correlated parameters of the incident beam and the maximal angle of the high numerical-aperture objective are investigated in deta il.Moreover,by adjusting relative parameters,the shape of the focus spot can be controlled,and the foc us spot can trap different particles by changing the corresponding parameter s.These results are quite important for many potential applications,such as optical trapping,optical data storage,particle acceleration,and particle t ransport.