The cross sections of e(+)e(-) -> pi(+) pi(-) hc at center-of-mass energies from 3.896 to 4.600 GeVare measured using data samples collected with the BESIII detector operating at the Beijing Electron Positron Collider. The cross sections are found to be of the same order of magnitude as those of e(+)e(-) -> pi(+) pi(-) J/psi and e(+)e(-) -> pi(+) pi(-) psi (2S), but the line shape is inconsistent with the Y states observed in the latter two modes. Two structures are observed in the e(+)e(-) -> pi(+) pi(-) hc cross sections around 4.22 and 4.39 GeV/c(2), which we call Y(4220)and Y(4390), respectively. A fit with a coherent sum of two Breit-Wigner functions results in a mass of (4218.4(- 4.5)(vertical bar 5.5) +/- 0.9) MeV/ c(2) a...