A new model named the coupled-oscillator model, in which the relationship of the lateral force and the normal force are considered, is proposed for studying the interfacial friction. The Maugis-Dugdal model is used to approximately substitute the Lennard-Jones potential of the interfacial friction in the new model. Then, the formulas for frictional force calculation are deduced. Comparison between the theoretical results and the experimental data obtained by an atomic force microscope shows that the model and the formulas are practically feasible. Based on the coupled-oscillator model, it is found that the frictional force increases approximately with the 2/3th power of the normal force for a tip-sample contact system, which is the same as the classical conclusion of nano-tribology.