In the last decade, interest in projective MV-algebras has grown greatly; see Cabrer and Mundici (Algebra Univ 62(1):63–74, 2009), Di Nola et al. (Int J Approx Reason 47(3):323–332, 2008) and Di Nola and Grigolia (J Multiple-Valued Logic Soft Comput 9(3):291–317, 2003). In this paper, we establish a necessary and sufficient condition for $$n$$ elements of the free $$n$$ -generator MV-algebra to generate a projective MV-algebra. This generalizes the characterization of the $$n$$ free generators proved in Lacava (Algebra Univ 57(4):455–462, 2007). Using this, some classes of projective generators for bigenerated MV-algebras, are given. In particular, some effective procedures to determine, by elementary methods, generators of projective MV-algebras are explained.