The properties of speckle field is studied when Laguerre-Gaussian (LG) beams illuminate a ground glass plate. The LG vortex beams are generated by a spatial light modulator combing with computer-generated hologram. The relation of speckle size and azimuthal and radial indices and the bright region of the LG beams are analyzed experimentally. Experimental results show that the speckle size decreases linearly with the azimuthal index increasing for certain radial index. Similarly, the speckle size also decreases with the radial index increasing for certain azimuthal index. Moreover, the speckle size is proportional to the negative factor of illuminating area of the LG beam. Further, the negative factor is gradual close to the results of Gaussian beam illuminating with the increasing radial index.