When casting wet concrete into hollow steel tubular arch during the construction process of a concrete-filled steel tubular arch bridge, an initial stress (due to dead load, etc.) would be produced in the steel tube. In order to understand the influence of this initial stress on the strength of the concrete-filled steel tubular arch bridge, a total of four single tubular arch rib (bare steel first) specimens (concrete-filled steel tubular last) with various initial stress levels were constructed and tested to failure. The test results indicate that the initial stress has a large influence on the ultimate load-carrying capacity and ductility of the arch structure. The high preloading ratio will reduce significantly the strength and ductility that the maximum reductions are over 25%. Then, a finite element method was presented and validated using the test results. Based on this finite element model, a parametric study was performed that considered the influence of various parameters on the ultimate load-carrying capacity of concrete-filled steel tubular arches. These parameters included arch slenderness, rise-to-span ratio, loading method, and initial stress level. The analysis results indicate that the initial stress can reduce the ultimate loading capacity significantly, and this reduction has a strong relationship with arch slenderness and rise-to-span ratio. Finally, a method for calculating the preloading reduction factor of ultimate load-carrying capacity of single concrete-filled steel tubular arch rib structures was proposed based on the equivalent beam–column method.