In this paper we obtain an analytical solution to the harmonic generation processes in a quasiperiodic optical superlattice. The derived theory was applied to an intergrowth optical superlattice made from a single crystal with laminar domain reversal to realize third-harmonic generation processes. The quasiperiodic structure can provide more reciprocal vectors to compensate for the phase mismatches of the optical parametric processes, which make most of the intense harmonic peaks labelled by the corresponding reciprocal vector indices. The dependence of the harmonic intensity spectrum on structure parameters is presented. Conditions for efficient third-harmonic generation are also discussed in detail.