With a sample of (10087 ± 44) × 106J/ψ events accumulated with the BESIII detector, we analyze the decays η′ → π+π−l+l−(l = e, μ) via the process J/ψ → γη′. The branching fractions are measured to be B(η′ → π+π−e+e−) = (2.45 ± 0.02(stat.) ± 0.08(syst.)) × 10−3 and B(η′ → π+π−μ+μ−) = (2.16 ± 0.12(stat.) ± 0.06(syst.)) × 10−5, and the ratio is Bη′→π+π−e+e−Bη′→π+π−μ+μ−=113.4±0.9stat.±3.7syst. In addition, by combining the η′ → π+π−e+e− and η′ → π+π−μ+μ− decays, the slope parameter of the electromagnetic transition form factor is measured to be bη′ = 1.30 ± 0.19 (GeV/c2)−2, which is consistent with previous measurements from BESIII and theoretical predictions from the VMD model. The asymmetry in the angle between the π+π− and l+l− decay planes, which has the potential to reveal the CP-violation originating from an unconventional electric dipole transition, is also investigated. The asymmetry parameters are determined to be ACPη′→π+π−e+e−=−0.21±0.73stat.±0.01syst.% and ACPη′→π+π−μ+μ−=0.62±4.71stat.±0.08syst.%, implying that no evidence of CP-violation is observed at the present statistics. Finally, an axion-like particle is searched for via the decay η′ → π+π−a, a → e+e−, and upper limits of the branching fractions are presented for the mass assumptions of the axion-like particle in the range of 0 − 500 MeV/c2.