A search for the CP -violating strong decays η→π+π− and η′(958)→π+π− has been performed using approximately 2.5×107 events of each of the decays D+→π+π+π− and View the MathML source, recorded by the LHCb experiment. The data set corresponds to an integrated luminosity of 3.0 fb−1 of pp collision data recorded during LHC Run 1 and 0.3 fb−1 recorded in Run 2. No evidence is seen for View the MathML source with η(′)→π+π−, and upper limits at 90% confidence level are set on the branching fractions, B(η→π+π−)<1.6×10−5 and B(η′→π+π−)<1.8×10−5. The limit for the η decay is comparable with the existing one, while that for the η′ is a factor of three smaller than the previous limit.