Direct optical fabrication of 3D photonic crystals in a high refractive index LiNbO3 crystal by using the femtosecond laser-induced microexplosion method is investigated. The focal distortion, caused by the refractive index mismatch-induced spherical aberration, can be significantly reduced by using a so-called threshold fabrication method. As a result, 3D fee photonic crystals are fabricated by stacking quasi-spherical voids layer by layer. Photonic stopgaps with suppression rates of up to 30% in the transmission spectra are observed. The angle dependence of the stopgaps is also revealed.