A partial wave analysis on the process e+e− → ωπ+π− is performed using 647 pb−1 of data sample collected by using the BESIII detector operating at the BEPCII storage ring at center-of-mass (c.m.) energies from 2.000 GeV to 3.080 GeV. The Born cross section of the e+e− → ωπ+π− process is measured, with precision improved by a factor of 3 compared to that of previous studies. A structure near 2.25 GeV is observed in the energy-dependent cross sections of e+e− → ωπ+π− and ωπ0π0 with a statistical significance of 7.6σ, and its determined mass and width are 2232 ± 19 ± 27 MeV/c2 and 93 ± 53 ± 20 MeV, respectively, where the first and second uncertainties are statistical and systematic, respectively. By analyzing the cross sections of subprocesses e+e− → ωf0(500), ωf0(980), ωf0(1370), ωf2(1270), and b1(1235)π, a structure, with mass M = 2200 ± 11 ± 17 MeV/c2 and width Γ = 74 ± 20 ± 24 MeV, is observed with a combined statistical significance of 7.9σ. The measured resonance parameters will help to reveal the nature of vector states around 2.25 GeV.