Complementary sequences have been applied to multi-carrier code-division multiple-access wireless communication systems. In this letter, multiple complementary sequence sets are constructed. The presented multiple complementary sequence sets have the following properties: first, each set is a complete complementary code (CCC) with parameters (p,p,p)-CCC; second, the maximum inter-set aperiodic cross-correlation amplitude is p; and finally, an aperiodic quasi-complementary sequence set with asymptotically near optimal correlation amplitude will be obtained by combining these complementary sequence sets together, which is not covered in the literature.