In this study, we present a novel organic hybrid Ni-based δ-isomer of Anderson-type polyoxometalates (POMs), namely, δ-[C6H12Mo6N2NiO24]4− (1), as an efficient catalyst for the cycloaddition reaction between alkynes, halides, and sodium azide. Synthesis of the catalyst was performed using a facile one-pot method followed by characterization using single crystal, powder XRD, SEM, and FT-IR techniques. After optimizing reaction conditions for a model reaction (T = 80 °C, time = 6 h, and solvent = 2 mL H2O), the catalytic activity of this compound was examined for the preparation of diversely substituted 1,2,3-triazoles under ambient atmospheric and additive-free conditions, achieving moderate to good yields. Catalyst 1 could reuse up to four sequential cycles without significant loss in its catalytic activity. Additionally, the true heterogeneity of the catalyst was determined by the hot-filtration test.