Fully developed turbulent flows in a duct of square cross section are numerically simulated by the LES technique using 160, 000 computational grid points. Reynolds numbers based on the bulk velocity and the duct width are 6, 200 and 67, 400. The representative secondary motion near the corner is reasonably reproduced. The near wall behavior of the Reynolds stress and the corresponding pressure field obtained by LES have elucidated the mechanism of the turbulence-driven secondary flow. The essential factor is the rapid attenuation of the turbulence stress due to the wall effect. The pressure distribution, on the other side, has the gradient along the wall. The imbalance between them causes the secondary motion.