Recent findings suggest that i) children can build initial verb entries on the basis of syntactic information alone without any additional information provided by a visual context, and ii) that the early representation of verbs encompasses statistical information on the co-occurrence of these verbs with their potential meanings/referents, enabling children to infer verb meanings under referential uncertainty. In this paper we present a computational model that acquires verb-general constructions under referential uncertainty. The model stores linguistic knowledge in line with construction grammar in the form of an interrelated network of constructions. Learning proceeds in line with usage-based theories in an item-based fashion. Computational results show that the model can account for the above-mentioned findings: The model produced patterns similar to those observed in these studies. Our findings hence shed light on the potential mechanisms involved in the emergence of early verb entries and verb-general constructions as well as the representation and refinement of verb entries