The reflective high-energy electron diffraction (RHEED) patterns were obtained during the growth of GaN by metal-organic molecular beam epitaxy (MOMBE). The lattice relaxation of GaN layers was observed during the initial growth at growth temperature. The estimated lattice constant along the a-axis using the RHEED patterns shows that the GaN layer undergoes compressive strain at the growth temperature after the growth. On the other hand, the lattice constant along the c-axis estimated using the X-ray diffraction peak revealed that the layer undergoes tensile strain. These results indicate that the strain in GaN layers at room temperature was introduced by the difference in the thermal expansion coefficients between GaN and 6H-SiC.