Abstract: Dynamic type information of ciphertext can be modified properly so that it can be well applied in a practical cloud storage environment. In order to meet the application requirements, Liu et al proposed a dynamic type and identity-based proxy re-encryption (PRE) scheme based on Ibraimi et al's scheme. Their scheme not only keeps the traditional core function of PRE scheme, but also makes sure that the owner of ciphertext can modify the type information at any time. However, after careful security analysis it found that Liu et al.'s scheme has two security flaws. Firstly, the dynamic type information lacks of verification, the adversary can modify the type tag. Secondly, the dynamic type information causes a conditional chosen plaintext attack. Thus we further improve Liu et al.'s scheme and give the security analysis.