We extend the concept of quasi-variety of first-order models from classical logic to multiple valued logic and study the relationship between quasi-varieties and existence of initial models in MVL. We define a concept of ‘Horn sentence’ in MVL and based upon our study of quasi-varieties of MVL models we derive the existence of initial models for MVL ‘Horn theories’. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.