The slightly enlarged and significantly more powerful B-58B was proposed by Convair as a follow-on to the B-58A. The B-58B was to be powered by four General Electric J79-GE-9 turbojets, which would have offered consierably more thrust than the J79-GE-5Bs of the B-58A. The B-58B would also have been significantly longer that the B-58A, with an extra structural section being inserted in the fuselage. The B-58B was also to have featured some aerodynamic refinements, with extensions being added to the inboard leading edges of the delta wing, which would have improved the handling characteristics at high angles of attack.
Perhaps the most significant difference between the B-58B and the earlier B-58A was to have been in the B-58B being able to offer many more weapons options than the B-58A. In particular, the B-58B was to have had a significant conventional weapons capability, which the B-58A did not have. This was to have been made possible by fitting a new and significantly larger underfuselage pod capable of carrying more fuel plus the ability to carry a set of conventional iron bombs in an internal bay. In addition, it was proposed that a pair of air-launched ballistic missiles be carried on underwing pylons just outboard of the centerline pod. Alternatively, an extra pair of fuel tanks could be carried on these underwing pylons.
B-58A serial number 55-0668 was to have been converted as a test aircraft for the B-58B program, and a prototype B-58B (60-1109) was actually ordered, but the B-58B project was cancelled before anything could be completed.