Crystal properties of wurtzite GaN films grown on $Al_2O_3$(0001) substrates under various nitrogen pressure and plasma power by electron cyclotron resonance molecular beam epitaxy were investigated by full width at half maximum of X-ray diffraction peak and scanning electron microscope. It was found that the nitrogen pressure has a large effect on the FWHM value of XRD, and the GaN film grown under the optimum nitrogen pressure contains high density of dislocations. These results suggest that the crystal quality is sensitive to the plasma source conditions and that the relaxation of stress depends of V/III ratio. However, substrate-surface nitridation has little effect on the relaxation of misfit stress.