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In this paper a Lattice Bhatager-Gross-Krook (LBGK) model to simulate incompressible flow is developed.The basic idea is to explicitly eliminate the compressible effect, due to the density fluctuation in the existing LBGK models.In the proposed incompressible LBGK model, the pressure p instead of the constant mass density ρ0 is the independent dynamic variable.The incompressible Navier-Stokes equations are exactly derived from this incompressible LBGK model.In order to test the LBGK model, the plane Poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as the 2-D Womersley flow are simulated.The numerical results are found to be in excellent agreement with theory and the results of previous studies.