Memory is essential to many cognitive tasks including language. Apart from empirical studies of memory effects on language acquisition and use, there lack sufficient evolutionary explorations on whether a high level of memory capacity is prerequisite for language and whether language origin could influence memory capacity. In line with evolutionary theories that natural selection refined language-related cognitive abilities, we advocated a coevolution scenario between language and memory capacity, which incorporated the genetic transmission of individual memory capacity, cultural transmission of idiolects, and natural and cultural selections on individual reproduction and language teaching. To illustrate the coevolution dynamics, we adopted a multi-agent computational model simulating the emergence of lexical items and simple syntax through iterated communications. Simulations showed that: along with the origin of a communal language, an initially-low memory capacity for acquired ling)