A new functionalized graphdiyne-based structure was designed by adsorbing single and double AM3O (AM = Li, Na, K) on graphdiyne (GDY) surface, namely (AM3O)n@GDY (AM = Li, Na, K; n = 1, 2). Density-functional theory calculations have been used to unravel the relations between the geometric structure and nonlinear optical (NLO) properties, e.g., Hyper-Rayleigh Scattering coefficient (βHRS) and nonlinear refractive index (n2). The frequency-dependent electro-optic Pockel's effect (EOPE) and second-harmonic generation (SHG) were explored to design the efficient NLO materials. Our calculations reveal that the AM3O molecule has the strong interactions with the GDY unit, and the intramolecular charge transfer is significant for determining the NLO properties. Large first hyperpolarizabilities (βtot) for single-adsorbed GDY have been found, especially for K3O@GDY (∼3.06 × 105 a.u.), rather than double-adsorbed GDY. Moreover, the small transition energies with large oscillator strength are a decisive factor for enhancing the βtot values. In the dynamic NLO process, the EOPE and SHG resonances can be enhanced at ω = 0.10 a.u., while single-adsorbed GDY clusters have large nonlinear refractive index and improved Hyper-Rayleigh Scattering response. All of these results will inevitably stimulate further synthesis of GDY-based optoelectronic materials with high NLO properties for future applications.