Induction of broadly neutralizing antibodies (bnAbs) is a primary goal of HIV vaccine development. VRC01-class bnAbs are important vaccine leads because their precursor B cells targeted by an engineered priming immunogen are relatively common among humans. This priming immunogen has demonstrated the ability to initiate a bnAb response in animal models, but recall and maturation toward bnAb development has not been shown. Here, we report the development of boosting immunogens designed to guide the genetic and functional maturation of previously primed VRC01-class precursors. Boosting a transgenic mouse model expressing germline VRC01 heavy chains produced broad neutralization of near-native isolates (N276A) and weak neutralization of fully native HIV. Functional and genetic characteristics indicate that the boosted mAbs are consistent with partially mature VRC01-class antibodies and place them on a maturation trajectory that leads toward mature VRC01-class bnAbs. The results show how reductionist sequential immunization can guide maturation of HIV bnAb responses.