Bound states in the continuum (BICs) have gained significant attention in recent years for enhancing light–matter interaction. Here, we numerically and experimentally demonstrate quasi-BICs in a terahertz photonic crystal (PhC) slab induced by breaking the structural symmetry. The terahertz PhC slab can support four symmetry-protected BICs, exhibiting multipole properties in the near fields and vector vortex characteristics in the far fields. By altering the shape of the holes to break the in-plane inversion symmetry, the quasi-BICs can be excited in the PhC slab under normal incidence. Furthermore, by elaborately adjusting the asymmetry parameter, accidental BICs can also be created in the asymmetric PhC slab. Experimental fabrication of both symmetric and asymmetric terahertz PhC slabs confirms the observation of quasi-BICs in the PhC slabs. The high-Q quasi-BICs in the asymmetric terahertz PhC slab show promise for applications in terahertz sensors, filters, and modulators.