Using a sample of 1.3 × 10(9) J/ψ events collected with the BESIII detector, we report the first observation of η(')→π(+)π(-)π(+)π(-) and η(')→π(+)π(-)π(0)π(0). The measured branching fractions are B(η(')→π(+)π(-)π(+)π(-)) = [8.53 ± 0.69(stat.) ± 0.64(syst.)]×10(-5) and B(η(')→π(+)π(-)π(0) π(0)) = [1.82 ± 0.35(stat.) ± 0.18(syst.)] × 10(-4), which are consistent with theoretical predictions based on a combination of chiral perturbation theory and vector-meson dominance.