Conventional methods for humanizing animal-derived antibodies involve grafting their complementarity-determining regions onto homologous human framework regions. However, this process can substantially lower antibody stability and antigen-binding affinity, and requires iterative mutational fine-tuning to recover the original antibody properties. Here we report a computational method for the systematic grafting of animal complementarity-determining regions onto thousands of human frameworks. The method, which we named CUMAb (for computational human antibody design; available at http://CUMAb.weizmann.ac.il ), starts from an experimental or model antibody structure and uses Rosetta atomistic simulations to select designs by energy and structural integrity. CUMAb-designed humanized versions of five antibodies exhibited similar affinities to those of the parental animal antibodies, with some designs showing marked improvement in stability. We also show that (1) non-homologous frameworks are often preferred to highest-homology frameworks, and (2) several CUMAb designs that differ by dozens of mutations and that use different human frameworks are functionally equivalent.