During the growth of graphene via chemical vapor deposition, its recessive process, that is, etching, is often neglected. However, recent experimental studies showed that etching is not only able to give rise to complex morphologies that cannot be achieved by pure growth, but it also can be used to create designed patterns. In this work, we develop a kinetic Monte Carlo model based on the underlying mechanisms and growth kinetics of graphene to predict the formation of various morphologies during growth and etching. The simulation results reproduce a variety of experimentally observed morphologies of graphene domains with six-fold, four-fold and three-fold symmetries. In addition, we propose analytical relations between the gas flow rate in the experiments and the growth and etching parameters used in our simulations. We also present a phase diagram for the domain morphology from the attachment-limited regime to the diffusion-limited regime to guide the control of domain morphology. The present study not only presents a viable model to simulate the morphological evolution of graphene domain, but also provides essential guidance to control graphene pattern formation for specific applications.