With discretized particle velocity space, a unified gas-kinetic scheme for entire Knudsen number flow is constructed based on the model Boltzmann equation. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate solution in the continuum flow regime with the time step being much larger than the particle collision time, and to capture rarefied flow phenomena as well. The unified scheme is an extension of the gas-kinetic BGK method for the Navier-Stokes solution to the rarefied flow regime with the discretization of particle velocity space. The success of the method is due to the coupled treatment of particle transport and collision in the evaluation of local time-dependent gas distribution function at a cell interface, and this coupling is crucial to avoid the requirement of time step being less than the particle collision time in a standard .kinetic equation solver. The physical reason will be pointed out and many numerical examples will be presented.