The interfacial Dzyaloshinskii-Moriya interaction (DMI) is an essential ingredient for stabilizing chiral spin configurations in spintronic applications. Here, via first-principles calculations, we reveal the influence of lattice strain on DMI in Co/Pt interface. We observed a considerable enhancement for a certain lattice strain. Furthermore, a direct correlation is established between the DMI and interlayer distances dominated by the strain, which is attributed to a hybridization of electronic orbitals. This hybridization has also been presented as the microscopic origin of the interfacial DMI. We anticipate that our predictions provide new insights into the control of interfacial DMI for skyrmion-based spintronic devices.