The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations.The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters such as the boundary layer growth, the shear rate, the boundary layer thickness, and the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure to investigate the boundary layer parameters inside the converging geometries.