It is often claimed that languages with more non-native speakers tend to become morphologically simpler, presumably because non-native speakers learn the language imperfectly. A growing number of studies support this claim, but there is a dearth of experiments that evaluate it and the suggested explanatory mechanisms. We performed a large-scale experiment which directly tested whether imperfect language learning simplifies linguistic structure and whether this effect is amplified by iterated learning. Members of 45 transmission chains, each consisting of 10 one-person generations, learned artificial mini-languages and transmitted them to the next generation. Manipulating the learning time showed that when transmission chains contained generations of imperfect learners, the decrease in morphological complexity was more pronounced than when the chains did not contain imperfect learners. The decrease was partial (complexity did not get fully eliminated) and gradual (caused by the accumulation of small simplifying changes). Simplification primarily affected double agent-marking, which is more redundant, arguably more difficult to learn and less salient than other features. The results were not affected by the number of the imperfect-learner generations in the transmission chains. Thus, we provide strong experimental evidence in support of the hypothesis that iterated imperfect learning leads to language simplification.