Low-speed gas flows in micro-channels are investigated using a kinetic theory analysis. The Boltzmann equation simplified by a collision model is solved by means of a finite difference approximation with the discrete ordinate method. Calculations are made for flows in simple micro-channels and a micro-fluidic system consisting of two micro-channels in series. The results are compared well with those from the DSMC method and an analytical solutions to the Wavier-Stokes equations. It is shown that the present method is a useful tool for the modeling of low-speed flows in micro-channels.