A vaccine that elicits broadly neutralizing antibodies (bNAbs) against HIV-1 is likely to be protective, but this has not been achieved. To explore immunization regimens that might elicit bNAbs, we produced and immunized mice expressing the predicted germline PGT121, a bNAb specific for the V3-loop and surrounding glycans on the HIV-1 spike. Priming with an epitope-modified immunogen designed to activate germline antibody-expressing B cells, followed by ELISA-guided boosting with a sequence of directional immunogens, native-like trimers with decreasing epitope modification, elicited heterologous tier-2-neutralizing responses. In contrast, repeated immunization with the priming immunogen did not. Antibody cloning confirmed elicitation of high levels of somatic mutation and tier-2-neutralizing antibodies resembling the authentic human bNAb. Our data establish that sequential immunization with specifically designed immunogens can induce high levels of somatic mutation and shepherd antibody maturation to produce bNAbs from their inferred germline precursors.