Abstract Two types of bound states in continuum (BICs), symmetry-protected and Brillouin zone folding driven, are identified in the hollow Si nanorod arrays. By modulating the direction and distance of the air holes from the center of the nanorods, it is possible to achieve either a single quasi-BIC or three quasi-BICs. The transmission spectra exhibit ultra-narrow lines, and the quasi-BICs demonstrate ultra-high Q factors. Additionally, effcient third-harmonic generation occurs at low pump intensities. The results indicate that the proposed nanostructures of two types of BICs with a flexible modulation hold great potential applications for nonlinear photonic devices.