Joint attention (JA) is important to many social, communicative activities, including language, and humans exhibit a considerably high level of JA compared with non-human primates. We propose a coevolutionary hypothesis to explain this degree-difference in JA: once JA started to aid linguistic comprehension, along with language evolution, communicative success (CS) during cultural transmission could enhance the levels of JA among language users. We illustrate this hypothesis via a multi-agent computational model, where JA boils down to a genetically transmitted ability to obtain non-linguistic cues aiding comprehension. The simulation results and statistical analysis show that: (i) the level of JA is correlated with the understandability of the emergent language; and (ii) CS can boost an initially low level of JA and 'ratchet' it up to a stable high level. This coevolutionary perspective helps explain the degree-difference in many language-related competences between humans and non-human primates, and reflects the importance of biological evolution, individual learning and cultural transmission to language evolution.