Many existing grid-based semi-Lagrangian approach are based on one-dimensional splitting,which is subject to splitting errors.We will propose a multi-dimensional strategy of tracing characteristics without splitting.It is high order in time via a prediction-correction approach.WENO interpolation is then used to recover function values with accurately located foot of characteristics between grid points.The algorithm does not have time step restrictions.The application to incompressible Euler equations will demonstrate its good performance.