This paper is the continuity of Guo's work [Phys.Rev., 2009, 046708] about a lattice Boltzmann model for axis-symmetric flows. This is a radius weighted LBM model: all the moments are proportional to the radial coordinate r. A Taylor series analysis is performed on the discrete Boltzmann Model in order to assess the consistency. The truncation error terms do not indicate any error increase along the radial direction, but they contain a spurious term u r /r which considerably reduces the model accuracy when radial velocity is non-null: simulation results highlight a reductions of the order of accuracy (from second to first). A new axis boundary condition was created to improve the model accuracy and to cope with the spurious error term. It was assessed though several test cases.