This paper introduces a novel approach to design acoustic metasurfaces utilizing multiple nonlinear spring oscillator chains, which enables an exceptional ability to generate harmonics in the radiated sound field. The metasurface unit is a chain of masses connected by two nonlinear springs exhibiting two resonance frequencies. The fundamental and second harmonic components of the vibration amplitude are solved by the Multiple Scales Method (MSM). By strategically configuring the higher resonance frequency of the spring oscillator to be n times that of the lower frequency and exciting the system with the lower frequency, the energy transfers from the low-frequency mode to the high-frequency mode induced by nonlinearity, leading to the large vibration amplitude of the high-frequency mode. The robustness and validity of this method are substantiated through the excellent consistency between the theoretical and numerical results. Furthermore, we showcase a nonlinear metasurface with more high-harmonic transmission by judiciously adjusting the structural parameters. Parameter tuning including adjustments to the quadratic nonlinear coefficient, resonance frequency, and excitation frequency further underscores the robustness of this nonlinear system, providing insights for designing general nonlinear metasurfaces. Our work lays a solid foundation for realizing harmonics in nonlinear spring oscillators, extending the research scope of acoustic metasurfaces into nonlinear dynamics.