A novel lattice Boltzmann formulation for axisymmetric flows with swirl is pro- posed in vorticity-stream function variables. The present model solves the evolution equations for the azimuthal components of the velocity and vorticity coupled with the Poisson equation for the stream function. All three equations are solved by using source terms in a pseudo carte- sian lattice Boltzmann formulation (LBM) formulation, which are needed in order to modify the standard D2Q5 lattice model used in the study. Numerical results of the simulations of a lid-driven swirling flow in a confined cylindrical cavity shows good agreement between the proposed model and numerical and experimental data available in the literature.