An adaptive Cartesian method combined with the ghost cell method is proposed to solve problems of unsteady aircraft icing simulation in this paper. In the grid generation module, Cartesian method is used to generate the background grids around the clean and iced geometries. Boundary self-adaptive method is developed to update the grids as the ice accumulates and the geometry is changing over time. Besides, local encryption is carried out around the boundary grids in order to improve the prediction accuracy. An improved ray method is used to classify the grids into four types, named fluid grids, solid grids, boundary grids and ghost grids. The flow field is obtained by solving Euler equations, and the ghost cell method is introduced to provide the boundary conditions due to the non-body-fitted feature of Cartesian grids. Droplet trajectories are calculated using Lagrangian method. And a new and efficient droplet location judgment method is proposed to determine whether the droplet impinges on the surface. Besides, the ice accretion behaviors are predicted using Messinger model. With the method proposed in this paper, extensive numerical tests in various icing temperatures are simulated. And, the computational results are compared with test results. It can be seen that the proposed new method can predict the unsteady process of aircraft ice accretion and the compared results also show better agreements for both glaze and rime ice.