In the present study, the fully developed turbulent secondary flows inside rotating and non-rotating square duct are numerically simulated using the linear and nonlinear k–ω models. For non-rotating duct, an eight-vortex structure is well captured by the nonlinear k–ω model. For rotating duct, it is interesting to notice that the two vortices are generated when Ro = 0.05, four vortices are presented when Ro = 0.15, and two vortices appeared when the rotational speed is increased up to Ro = 0.35. Although the linear and nonlinear models all produce reasonable results, the different results are also exhibited with these models. For example, the nonlinear model produces a stable effect in the pressure side and predicts less distortion region than the linear model. In the suction side, the linear k–ω model produces greater gradients than the linear model which seems to be realistic.