Using a sample of (10087±44)×10^{6} J/ψ events, which is about 45 times larger than that was previously analyzed, a further investigation on the J/ψ→γ3(π^{+}π^{-}) decay is performed. A significant distortion at 1.84 GeV/c^{2} in the line shape of the 3(π^{+}π^{-}) invariant mass spectrum is observed for the first time, which could be resolved by two overlapping resonant structures, X(1840) and X(1880). The new state X(1880) is observed with a statistical significance larger than 10σ. The mass and width of X(1880) are determined to be 1882.1±1.7±0.7 MeV/c^{2} and 30.7±5.5±2.4 MeV, respectively, which indicates the existence of a pp[over ¯] bound state.