In this paper, we propose a micro-ring resonator model based on gallium nitride (GaN) and graphene, which exhibits tunable properties of nonlinearity. It provides a great bandwidth covering from visible to telecommunication band. Especially, based on the characteristic of GaN, it has unique advantages in shorter wavelength, which is used for demonstrating the ultrafast signal processing including wavelength conversion, temporal amplification and pulse compression. Moreover, the tunable signal processing is achieved via the method of applying additional bias voltage to graphene without changing the geometric dimension of the device. These results have significant potential applications of nonlinear optics and optical communications.