CLEFIA is a block cipher developed by Sony Corporation in 2007. It is a recommended cipher of CRYPTREC, and has been adopted as ISO/IEC international standard in lightweight cryptography. In this paper, some new 9-round zero-correlation linear distinguishers of CLEFIA are constructed with independent input masks and output masks, which admit multiple zero-correlation linear attacks on 14/15-round CLEAIA-192/256 about 79 times faster than results of the SAC paper with one-eighth of data. Furthermore, some new integral distinguishers over 9 rounds are derived by the relations between integral distinguishers and zero-correlation linear approximations. By using these integral distinguishers, the previous integral attacks on CLEFIA are improved with the partial sum technique. Our results have either one more rounds or lower time complexity than previous attack results with integral and zero-correlation linear cryptanalysis.