Due in part to the increasing availability of crystallographic protein structures as well as rapid improvements in computing power, the past few decades have seen an explosion in the field of computer-based rational drug design. Several algorithms have been developed to identify or generate potential ligands in silico by optimizing the ligand-receptor hydrogen bond, electrostatic, and hydrophobic interactions. We here present AutoGrow, a novel computer-aided drug design algorithm that combines the strengths of both fragment-based growing and docking algorithms. To validate AutoGrow, we recreate three crystallographically resolved ligands from their constituent fragments.