Concrete-filled steel tubular (CFST) support is an innovative and effective support technology, which has been broadly applied in underground roadways. However, failure is still possible, and the primary failure locations are commonly the vault and the springline. In order to reveal the failure mechanism and provide an effective solution, the inner forces of a circular CFST support were investigated analytically. To improve the flexural performance, firstly, the flexural behavior of CFST beams strengthened by welded steel at soffit was investigated experimentally. A total of 6 beams were tested under a four-point bending load, and the investigated parameter was welded steel diameter. The corresponding nonlinear three-dimensional finite element model was established in the ABAQUS software and was validated using the experimental results. Then, the effect of welded range and welded location on the support bearing performance was investigated numerically. Finally, the proposed method was validated by an application example. Results show that CFST support bearing performance is greatly improved when the lateral pressure coefficient is equal to 1.0, because there is no bending moment, and the thrust force is equally distributed along the perimeter of the support. When the lateral pressure coefficient is not equal to 1.0, the sections at vault, invert, and springline, where the maximum bending moments located, are the most vulnerable. Welding steel at locations dominant by the bending moment is an effective way to improve flexural bearing capacity. The optimal flexural strengthening method for the support is welding steel at the vault and the springline, respectively, named ‘three-arcs welding.’