Affinity improvement of proteins, including antibodies, by computational chemistry broadly relies on physics-based energy functions coupled with refinement. However, achieving significant enhancement of binding affinity (>10-fold) remains a challenging exercise, particularly for cross-reactive antibodies. We describe here an empirical approach that captures key physicochemical features common to antigen-antibody interfaces to predict protein-protein interaction and mutations that confer increased affinity. We apply this approach to the design of affinity-enhancing mutations in 4E11, a potent cross-reactive neutralizing antibody to dengue virus (DV), without a crystal structure. Combination of predicted mutations led to a 450-fold improvement in affinity to serotype 4 of DV while preserving, or modestly increasing, affinity to serotypes 1-3 of DV. We show that increased affinity resulted in strong in vitro neutralizing activity to all four serotypes, and that the redesigned antibody has potent antiviral activity in a mouse model of DV challenge. Our findings demonstrate an empirical computational chemistry approach for improving protein-protein docking and engineering antibody affinity, which will help accelerate the development of clinically relevant antibodies.