Under the dual challenges of the energy crisis and environmental pollution, the technology of photocatalytic water splitting for hydrogen production has become a research hotspot in clean energy due to its green and sustainable characteristics. As a novel quasi-one-dimensional semiconductor material, fibrous red phosphorene (FRP) exhibits remarkable photocatalytic hydrogen evolution potential, owing to its moderate bandgap, high carrier mobility, and excellent air stability. Based on first-principles calculations, we systematically investigated the regulatory mechanisms of a series of non-metallic elements X (B, C, N, O, Si, S, As, and Se) doping on the electronic structure and catalytic performance of single-layer FRP. The results show that the element X can effectively enhance the hydrogen evolution reaction (HER) activity of single-layer FRP. Among them, four doped systems (S-doped at site 1, B-doped at sites 1/2/5) exhibit excellent catalytic activity for HER. In particular, the B-doped system at site 2 has the most ideal free energy of hydrogen adsorption (ΔG_H*), and its overpotential (η = -0.074 V) is comparable to that of the noble metal Pt catalyst. Through the analysis of the electronic structure, it is found that the enhancement of the HER catalytic activity is closely related to the downward shift of the X pz-band center at the adsorption site. There is a direct proportional relationship between ΔG_H* and the X p_z-band center (R² ≥ 0.78), indicating that the X p_z-band center can serve as a key electronic descriptor for regulating the HER activity. Further verification by calculations using the HSE06 hybrid functional shows that the band edge positions of the B-doped system can span both sides of the redox potential of water, and the light absorption range covers the visible light region, indicating the thermodynamic feasibility and spectral response advantages of this system in the application of photocatalytic overall water splitting. This study provides important theoretical guidance for the design of efficient FRP-based photocatalytic materials based on the non-metallic doping strategy.