In this paper, we present a numerical study of the effect of slip in the fluid-particle interaction. The motion of the particle is described by the Newton's second law and the flows are simulated by solving the incompressible Navier-Stokes equations with the Navier slip boundary condition. Numerical schemes are designed using the extended finite element method (XFEM) combined with the temporary arbitrary Lagrangian-Eulerian (tALE) technique. In this method, both the fluid dynamics and the motion of particle are efficiently computed on a fixed Cartesian mesh. With the XFEM, the discontinuities at the particle boundary are naturally captured by the Heaviside-enriched finite element basis functions. With the tALE technique, field variables at the previous time level are mapped onto the computational mesh at the current time level, hence regeneration or deformation of meshes can be avoided. To study the effect of the slip, we simulate the rotation of an ellipsoidal particle in a simple shear flow and compare with the analytic results from the theory of Jeffery orbit.