The initial stage of the growth of GaAs on Si by, MOCVD, the reduction of the residual dislocations by annealing at high temperatures and the dependence of the growth temperature on the stress in the GaAs layer were studied. The density and the size of deposited GaAs islands at the initial stage of the growth in the two-step growth sequence strongly affected the domain property of the subsequently grown layer. For reducing the residual dislocations by annealing at high temperatures, to repeat the growth and the annealing was more effective method compared with the other annealing methods we tried. The stress in the GaAs layers showed a constant value independently of the growth temperature and the value was related to the thermal expansion between room temperature and about 350°C.