Gas flow in microchannels can often encounter tangential slip motion at the solid surface even under creeping flow conditions. To simulate low speed gas flows with Knudsen numbers extending into the transition regime, alternative methods to both the Navier–Stokes and direct simulation Monte Carlo approaches are needed that balance computational efficiency and simulation accuracy. The lattice Boltzmann method offers an approach that is particularly suitable for mesoscopic simulation where details of the molecular motion are not required. In this paper, the lattice Boltzmann method has been applied to gas flows with finite Knudsen number and the tangential momentum accommodation coefficient has been implemented to describe the gas-surface interactions. For fully-developed channel flows, the results of the present method are in excellent agreement with the analytical slip-flow solution of the Navier–Stokes equations, which are valid for Knudsen numbers less than 0.1. The present paper demonstrates that the lattice Boltzmann approach is a promising alternative simulation tool for the design of microfluidic devices.