This work investigates numerically a non-premixed swirling flame in a coaxial burner with a radial fuel injection under lean and rich conditions of mixtures. The swirler is placed in the annular part of the burner. The fuel is injected radially through eight holes symmetrically distributed on the periphery of the central tube. All simulations are carried out using the ANSYS-Fluent CFD code. The turbulence is captured using the Reynolds Averaged Navier-Stokes approach. Chemistry/turbulence interaction is resolved using the Eddy Dissipation Model. Simulations are performed with a global equivalence ratio ranging from 0.5 to 1.3. Model validation is achieved by comparing computed results to our experimental data of Stereoscopic Particle Image Velocimetry obtained in the case of the stoichiometric regime. Good agreement between numerical results and experimental measurements is assigned. The central recirculation zone and the swirling jet region due to the presence of the swirl are well predicted by the simulations. The effect of the global equivalence ratio on the profile of axial velocity, temperature distributions and pollutant emissions (CO and NOx) is numerically studied. From dynamic point of view, the equivalence ratio modifies the mean axial velocity of the swirling diffusion flame. The increase of equivalence ratio destabilizes the flame by increasing the liftoff height. NO production decreases by the increasing of the equivalence ratio.