Let q=3l+1 and q=3l+2 be prime powers. The maximal designed distances of imprimitive Hermitian dual containing q-ary narrow-sense (NS) and non-narrow-sense (NNS) BCH codes of length n=3(q－1)are determined, and a series of NS and NNS BCH codes are constructed and their parameters are computed. Consequently, two families of q-ary quantum BCH codes are derived from these BCH codes. Some of these quantum BCH codes constructed from NNS BCH codes have better parameters than those quantum BCH codes available in the literature.