The intensity and phase distributions of speckle fields on the near-field plane generated by the scattering of Laguerre-Gaussian beam from the weak random scattering screen are simulated. It is found that the spot profiles are similar to the peacock feather in intensity distributions of speckle fields, and those spots are uniformly distributed around the central dark spots. The number of spots is related to the orbital angular momentum quantum number of the vortex beams. The orbital angular momentum quantum number is an integer or fractional, while whether it is integer or fractional, the number spots is four times of the orbital angular momentum quantum number. In the case of fractional vortex beam, there is a spot along the horizontal direction uniformly split into two petals. This method can be used to detect the orbital angular momentum quantum number of vortex beams.