Due to their tunable material properties, binary colloidal crystals (BCCs) are highly desired for many of the same applications as colloidal crystals. Here, we have investigated the detailed growth process of BCCs with attractive interparticle interactions in which depletion forces were induced between particles via added polymer. An AB2 superlattice phase (A, large; B, small) was grown under various solution conditions, including various large-to-small particle ratios and polymer concentrations. The solution composition at which the AB2 phase initially nucleated shifted toward an A-rich composition as the polymer concentration increased because the free energy curves of AB2 and other phases displayed different trends. This indicates that interparticle interactions played an important role and depended on the particle structure. In situ observations revealed that BCCs typically grew via one-dimensional heteroepitaxy, which differs from conventional colloidal epitaxial growth, demonstrating a novel technique to control the growth of BCCs.