We report, for the first time, that the coherent growth of zinc sulfide (ZnS) on a colloidal indium phosphide (InP) quantum dot (QD) yields a InP/ZnS core/shell structure with a single lattice constant of 0.563 nm. Compared to the bulk crystal of zinc-blend (cubic) InP, the lattice of the core QD is compressed by 4.1%. In contrast, the lattice of the shell expands by 4.1% relative to the bulky ZnS crystal throughout the core/shell QD if the shell is thinner than or equal to 0.81 nm and the diameter of the core QD is smaller than 2.64 nm. Under these conditions, the bandgap of the core QD increases, resulting in a blueshift of absorption and photoluminescence (PL) spectra. The PL peak is centered at 523 nm. Furthermore, the PL quantum yield is enhanced up to 70% and the PL bandwidth narrows to 36 nm based on the strengthened quantum confinement effect. The temperature dependence of the PL properties is investigated to discuss the effect of the core/shell lattice coherency on the improved PL performances.