Current proxy signature schemes are mostly identity-based proxy signatures that distinguish users by identity. This signature method faces some problems, such as identity information leakage and single access control. Attribute-based proxy signature (ABPS) divides the signer’s identity information into a collection of attributes; thus, users’ identity information can be protected and access control can become fine-grained. With the development of quantum computers, the security of signature schemes based on traditional number theory problems is under threat. Therefore, we construct a new attribute-based proxy signature scheme on a lattice that can resist quantum attacks. This scheme has the properties of both attribute-based signatures and proxy signatures, i.e., fine-grained access control and strong undeniability properties. Moreover, based on the small integer solution problem (SIS), our scheme is provably secure in the random oracle model and protects the proxy signer in the adaptive security model.