In our previous work, the technique of generating cylindrical converging shock waves based on shock dynamics theory was proposed. In the present work, a further study is carried out to assess the influence of several parameters including the converging angle θ0, the incident planar shock Mach number M0, and the shock tube height h on the wall profile and the converging shock wave. Combining the high-speed schlieren photography and the numerical simulation with the shock dynamics theory, the characteristics of wall profiles, cylindrical converging shock waves, and thermodynamic properties for different controllable parameters are analyzed. It is found that these parameters have great effects on shapes of the wall profile and experimental investigation favors large values of M0 and h and moderate θ0. The experimental sequences of schlieren images indicate that the shocks moving in the converging part are of circular shapes, which further verifies the method in our previous work. In addition, the changes of the shock Mach number, pressure, temperature, and density are obtained quantitatively. The results show that higher pressure and temperature can be reached in the converging part at the same distance to the center of convergence for larger incident shock Mach numbers, larger shock tube heights, or smaller converging angles. All the database will be useful for understanding the shock focusing and further investigating the Richtmyer-Meshkov instability induced by the converging shock waves.