The discontinuous-grid method can greatly reduce the storage requirements and computational costs of finite-difference (FD) modeling for large-velocity-contrast models. However, traditional discontinuous-grid methods have to use interpolation when refining the wavefield in transition zones and would cause apparent artifacts. We have developed a new discontinuous collocated-grid scheme for high-order FD modeling. We refined the wavefield on a rotated coordinate system, where the interpolation is not required again. The horizontal and vertical spatial derivatives can be accurately converted into diagonal derivatives within the rotated coordinate system; thus, our scheme would be free of artifacts caused by improper interpolation. The ratio from coarse- to fine-grid spacing is restricted to for our scheme, where is a positive integer. Numerical experiments demonstrate that the proposed discontinuous collocated-grid scheme reduces the artificial reflections by about two orders of magnitude compared to the interpolation scheme and yields a wavefield that is almost identical to that of the uniform-grid simulation. The rotated FD operator with arbitrary even-order accuracy is applied in the transition zones; thus, it significantly improves the spatial accuracy while saving computational cost.