The solar composition problem has puzzled astrophysicists for more than 20 years. Recent measurements of carbon-nitrogen-oxygen (CNO) neutrinos by the Borexino experiment show a ∼2σ tension with the "low-metallicity" determinations. ^{14}N(p,γ)^{15}O, the slowest reaction in the CNO cycle, plays a crucial role in the standard solar model (SSM) calculations of CNO neutrino fluxes. Here we report a direct measurement of the ^{14}N(p,γ)^{15}O reaction, in which S-factors for all transitions were simultaneously determined in the energy range of E_{p}=110-260 keV for the first time. Our results resolve previous discrepancies in the ground-state transition, yielding a zero-energy S-factor S_{114}(0)=1.93±0.10 keV b, which is 15% higher than the 1.68±0.14 keV b recommended in Solar Fusion III (SF-III). With our S_{114} values, the SSM B23-MB22p, and the latest global analysis of solar neutrino measurements, the C and N photospheric abundance determined by the Borexino experiment is updated to N_{CN}=(4.42_{-0.63}^{+0.70})×10^{-4}. This new N_{CN} value agrees well with latest "high-metallicity" composition; however, it is also consistent with the "low-metallicity" determination within ∼1σ CL, indicating that the solar metallicity problem remains an open question. In addition, the significant reduction in the uncertainty of S_{114} paves the way for the precise determination of the CN abundance in future large-volume solar neutrino measurements.