A particle-resolved direct numerical simulation is performed on the motion of spherical particles with an eccentric internal mass distribution in lateral linear shear flow, which is oriented in the vertical direction and sheared in a horizontal direction. We examine the effect of mass eccentricity on the two-way interactions of particles with both laminar and turbulent shear flows. A spherical shell/hollow particle with an inner spherical core is focused on as a typical example of mass eccentric particles. The Navier–Stokes equations and the Newton–Euler equations are solved for the fluid phase and the particles, respectively. An immersed boundary method is adopted to represent the shell particle. The Newton–Euler equations are solved using the body-fixed coordinate system and four quaternion parameters, considering the deviation of the center of mass from the center of the spherical shell particle. Simulations are performed at a relatively low particle volume fraction of 0.4%. In turbulent flows, the Taylor-microscale Reynolds number reached about 49 at the end of the simulations. Numerical results show that shear-induced particle rotation is suppressed by the torque due to gravity. It is found that the lateral migration of mass eccentric particles becomes less vigorous in both laminar and turbulent flows since the effect of the Magnus lift force is also weakened for mass eccentric particles. It is also found that the evolution of fluid kinetic energy is significantly affected by the mass eccentricity of particles in laminar flows.