The decays of J/psi --> etaphif(0)(980)[eta --> gammagamma, phi --> K(+) K(-), f(0)(980) --> pi(+)pi(-)] are analyzed using a sample of 5.8 x 10(7) J/psi events collected with the BESII detector at the Beijing Electron-Positron Collider. A structure at around 2.18 GeV/c(2) with about 5 sigma significance is observed in the phif(0)(980) invariant mass spectrum. A fit with a Breit-Wigner function gives the peak mass and width of m = 2.186+/-0.010(stat)+/-0.006(syst) GeV/c(2) and Gamma = 0.065+/-0.023(stat)+/-0.017(syst) GeV/c(2), respectively, which are consistent with those of Y(2175), observed by the BABAR Collaboration in the initial-state radiation process e(+)e(-) --> gamma(ISR) phif(0)(980). The production branching ratio is determined to be Br(J/psi --> etaY(2175))Br(Y(2175)- -> phif(0)(980))Br(f(0)(980) --> pi(+)pi(-)) = [3.23+/-0.75(stat)+/-0.73(syst)] x 10(-4), assuming that the Y(2175) is a 1(--) state.