We report the first observation of the decay $Lambda^+_{c}rightarrow Sigma^- pi^+pi^+pi^0$, based on data obtained in $e^+e^-$ annihilations with an integrated luminosity of 567~pb$^{-1}$ at $sqrt{s}=4.6$~GeV. The data were collected with the BESIII detector at the BEPCII storage rings. The absolute branching fraction $mathcal{B}(Lambda^+_{c}rightarrowSigma^-pi^+pi^+pi^0)$ is determined to be $(2.11pm0.33({rm stat.})pm0.14({rm syst.}))%$. In addition, an improved measurement of $mathcal{B}(Lambda^+_{c}rightarrowSigma^-pi^+pi^+)$ is determined as $(1.81pm0.17({rm stat.})pm0.09({rm syst.}))%$.