Antibodies are an important class of proteins with many biomedical and biotechnical applications. Although there are a plethora of experimental techniques geared toward their efficient production, there is a paucity of computational methods for their de novo design. OptCDR is a general computational method to design the binding portions of antibodies to have high specificity and affinity against any targeted epitope of an antigen. First, combinations of canonical structures for the antibody complementarity determining regions (CDRs) that are most likely to be able to favorably bind the antigen are selected. This is followed by the simultaneous refinement of the CDR structures' backbones and optimal amino acid selection for each position. OptCDR is applied to three computational test cases: a peptide from the capsid of hepatitis C, the hapten fluorescein and the protein vascular endothelial growth factor. The results demonstrate that OptCDR can efficiently generate diverse antibody libraries of a pre-specified size with promising antigen affinity potential as exemplified by computationally derived binding metrics.