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The singly Cabibbo-suppressed decay D+s → K+π+π−π0 is observed by using a data set corresponding to an integrated luminosity of 6.32 fb−1 recorded by the BESIII detector at the centre-of-mass energies between 4.178 and 4.226 GeV. The first amplitude analysis of D+s → K+π+π−π0 reveals the sub-structures in this decay and determines the fractions and relative phases of different intermediate processes. The dominant intermediate process is D+s → K∗0ρ+, with a fit fraction of (40.5 ± 2.8stat. ± 1.5syst.)%. With the detection efficiency based on our amplitude analysis, the absolute branching fraction forD+s → K+π+π−π0 is measured to be (9.75 ± 0.54stat. ± 0.17syst.) × 10−3.