An aggregate signature scheme,which is an extension of ordinary signature, allows anyone to compress n signatures of n messages from n signers into a single short signature for reducing the size multiple individual signatures. Recently, Liu et al. proposed an efficient certificateless aggregate signature scheme with shorter public key size, constant AS size and with constant pairing computations. Although they proved that the scheme has existential unforgeability against adaptive chosen messages attacks. However, in this paper, two concrete attacks are proposed to show that Liu et al.'s scheme actually does not reach the security as they claimed.