Grammar represents the most advanced element in human language. Language grammar requires a lexicon as a departing condition. It is proposed that three stages of language evolution can be distinguished: (a) Primitive communication systems using not only sounds but also gestures, grunts, etc., similar to those observed in non-human primates; (b) initial communication systems using a lexicon but without grammar; (c) complex communication systems including language grammar. It is suggested that grammar originates from the internal representation of actions resulting in the use of verbs; this ability depends on the Broca’s area (left inferior frontal gyrus) and related brain areas. The development of human language grammar is considered to be recent in human history. It is thought that grammar was developed in two steps: (a) Proto-grammar: verb-noun compounds used for naming; and (b) complex grammar, including diverse functional words. Finally, it is suggested that grammar represents the origin of complex cognition (“executive functionsµ).