A lattice Boltzmann method is developed for incompressible axisymmetric flows. Both force and source or sink terms are incorporated into the lattice Boltzmann equation in a natural way, which is consistent in dimension with the lattice Boltzmann equation. The correct macroscopic equations for incompressible axisymmetric flows are recovered through the Chapman-Enskog expansion. It turns out that the added terms are nothing but the additional in the governing equations for the axisymmetric flows compared with the Navier-Stokes equations, resulting in a simple and efficient model. This provides an additional unique advantage that the proposed scheme is naturally suitable for general axisymmetric flows involving more physical phenomena. Two numerical simulations have been presented to verify the method.