Certificateless aggregate signature (CLASS) scheme which combines on certificateless signature and aggregation signature solves the identity-based (ID) public key infrastructure (PKI)'s key escrow problem, the PK problem of traditional PKI. So, CLASS schemes can be applied in many fields to solve the privacy problem and security problem, for example in the information network and system of medicine and biology. Also there are many CLASS schemes to be proposed for these fields. In this manuscript, we analyze the CLASS scheme for VANETs proposed in 2018 which is more efficient than other similar schemes. We find which the CLASS scheme cannot satisfy the security the following two properties, namely unforgeability and traceability as they claimed. That is to say that the attacker may forge a correct signature and it may pass the signature verification but the attacker unknows the secret key. So, the CLASS scheme is not suitable for applying in any system. As an improving, after analyzing original scheme, it is found that the key problems for being insecure and give one simple method to solve the existed drawbacks.