The design of nonlinear photonic Vogel’s spiral based on quasi-crystal theory was demonstrated. Two main parameters of Vogel’s spiral were arranged to obtain multi-reciprocal circles. Typical structure was fabricated by the near-infrared femtosecond laser poling technique, forming a nonlinear photonic structure, and multiple ring-like nonlinear Raman–Nath second-harmonic generation processes were realized and analyzed in detail. The structure for the cascaded third-harmonic generation process was predicted. The results could help deepen the understanding of Vogel’s spiral and quasi-crystal and pave the way for the combination of quasi-crystal theory with more aperiodic structures.