Abstract In this paper the Navier-Strokes equations are solved for three-dimensional steady laminar flows in complex geometries using a nonorthogonal, nonstaggered coordinate system. The strong conservation form of the governing equations is discretized using a finite volume method. The pressure velocity coupling is ensured by using the pressure-weighted interpolation method to calculate the velocities at the faces of control volumes. The method was assessed by comparing the predicted results for six test cases in which analytical solutions or experimental data were available. They correspond to the transport of a scalar in a prescribed flow field, the flow through a square diffuser, the flow through a transforming elliptical duct, and the flow through an S-shaped duct. The predictions reveal good agreement with available data, demonstrating the accuracy and generality of the present method.