In this work, we study a composite zinc oxide photonic crystal that includes a meso-cavity coupled to a photonic crystal L3 microcavity to obtain a double resonance effect and second-harmonic generation conversion efficiency as high as 468 W-1. This exceptional conversion efficiency was attributed to the high quality-factors Q found in the fundamental and second-harmonic modes whose values were of the order of 105 and 106, respectively. Since the L3 microcavity plays a relevant role in the second-harmonic generation of the composite photonic crystal, we performed a calculation of its photonic band structure to observe the induced modes in its bandgap. Furthermore, we also found that the resonant mode adjusted to the frequency of the second-harmonic exhibits high Purcell factors of the order of 105. Hence, in a semiconductor material, it can be easily enhanced the light emission at the second harmonic frequency using an adequate driving fundamental frequency light beam. These results can stimulate the engineering of photonic nanostructures in semiconductor materials to achieve highly efficient non-linear effects with applications in cavity Quantum Electrodynamics.