The coaxial jet consisting of swirl jet and axial jet plays a critical role in the industrial processes but is rarely investigated; therefore, it is numerically explored by means of the computational fluid dynamics (CFD) approach in the present work. The force on the swirler, axial and tangential velocity at the annular pipe outlet, and the spatial distribution of swirl number (SN) are selected to evaluate the effect of geometrical parameters on the swirling performance. The results clarify that the velocity and their azimuthal components in the transverse cross‐section can be categorized into six segments based on high/low velocity values. The coaxial jets form a weak swirl with high axial, certain tangential, and low radial velocities. x‐ and y‐vorticity vary within −200 to 200 s−1. Coaxial jet mixing decays the SN. Based on the multi‐objective matrix analysis, swirler height has the largest effect on swirl performance followed by diameter, angle, and number based on analysis. Optimal parameters are 130° vane angle, 240 mm diameter, 10 vanes, and 250 mm height of the swirler.