Large Eddy Simulations (LES) were carried out to investigate the aerodynamic characteristics of a rectangular cylinder with side ratio B/D=5 at Reynolds number Re=22,000 (based on cylinder thickness). Particular attention was devoted to the effects of velocity shear in the oncoming flow. Time-averaged and unsteady flow patterns around the cylinder were studied to enhance understanding of the effects of velocity shear. The simulation results showed that the Strouhal number has no significant variation with oncoming velocity shear, while the peak fluctuation frequency of the drag coefficient becomes identical to that of the lift coefficient with increase in velocity shear. The intermittently-reattached flow that features the aerodynamics of the 5:1 rectangular cylinder in non-shear flow becomes more stably reattached on the high-velocity side, and more stably separated on the low-velocity side. Both the mean and fluctuating drag coefficients increase slightly with increase in velocity shear. The mean and fluctuating lift and moment coefficients increase almost linearly with velocity shear. Lift force acts from the high-velocity side to the low-velocity side, which is similar to that of a circular cylinder but opposite to that of a square cylinder under the same oncoming shear flow.