Using the first principle method within the local spin density approximation, both the magnetism of defect induced in GaN and the effect of Si codoping on the magnetism in GaN with defect were investigated. It was found that defectinduced intrinsic magnetic moment of GaN is 3μB, while the magnetic moment is quenched to 2μB in Sicodoping GaN:Si. The magnetic moment decreases with the increase of the concentration of Si. The result is very helpful for experiments.