Based on (10087±44)×106 J/ψ events collected with the BESIII detector, the process J/ψ→γπ+π-η′ is studied using two largest decay channels of the η′ meson, η′→γπ+π- and η′→ηπ+π-, η→γγ. A new resonance, which we denote as the X(2600), is observed with a statistical significance larger than 20σ in the π+π-η′ invariant mass spectrum, and it has a connection to a structure around 1.5 GeV/c2 in the π+π- invariant mass spectrum. A simultaneous fit on the π+π-η′ and π+π- invariant mass spectra with the two η′ decay modes indicates that the mass and width of the X(2600) state are 2618.3±2.0-1.4+16.3 MeV/c2 and 195±5-17+26 MeV, where the first uncertainties are statistical, and the second systematic. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.