In this paper, the lateral migration of a neutrally buoyant spherical particle in a pressure-driven rectangular shaped channel flow of Giesekus viscoelastic fluids is numerically investigated with a fictitious domain method. The particle trajectories are shown for the channel aspect ratio 2, the ratio of the particle diameter to the channel height 0.15, the Reynolds number 1 and 50, and the Weissenberg number up to 2.5. When the fluid inertial effect is negligible, the particle migrates toward the channel centerline or the closest corner depending on its initial position, and the corner-attraction region is enlarged as the Weissenberg number increases. When both fluid inertial and elastic effects are important, most particles migrate toward the face centers of the shorter walls. The particle migration trajectories are significantly affected by the secondary flow.