In this paper, the effect of acceleration of runaway electrons on the microscopic instabilities is discussed. The result shows that the mechanism of instabilities is no longer a simple wave-particle resonant effect. When the resonant velocity is far away from the boundaries of the velocity region of runaway electrons, the growth rate is not considerably different from that in the no acceleration case. However, if it is close to the boundaries, the effect of acceleration on the growth rate will be important.