For an integer q≥2, new sets of q-phase aperiodic complementary sequences (ACSs) are constructed by using known sets of q-phase ACSs and certain matrices. Employing the Kronecker product to two known sets of q-phase ACSs, some sets of q-phase aperiodic complementary sequences with a new length are obtained. For an even integer q, some sets of q-phase ACSs with new parameters are generated, and their equivalent matrix representations are also presented.