Numerical simulations of fully-developed turbulent flow through a straight square duct at three Reynolds numbers of 190, 300, and 550 based on the friction velocity averaged over the duct perimeter and duct half width are reported. The effect of Reynolds number on the mean and turbulence statistics and secondary flow is investigated. The mean streamwise-velocity profiles along the wall bisector are found to obey a logarithmic scaling when they are normalized by the friction velocity at the mid-wall. Magnitudes and spatial distributions of the peak production and diffusion terms in the mean streamwise-vorticity equation normalized by the wall units are found to be unaffected by the Reynolds-number variation when they are considered in wall-unit coordinates.