The development of the Internet of Things (IoT) has been facing severe security threats, and the security and fine-grained access control of data in the IoT is one of the security problems that urgently need to deal with. Attribute-based encryption (ABE) schemes over lattice can not only achieve fine-grained access control but also resist quantum attacks. However, most schemes are single-bit encryption, which is inefficient. In this study, a multibit inner product predicate encryption (PE) scheme over lattice is proposed, which effectively expands the plaintext space. The scheme can realize multibit attribute-based encryption with the hidden access structure for data security in the IoT and support And-gate operation in the access structure with multiattribute. The fine-grained access control of ciphertext data can be realized under the condition of ensuring data privacy. The security of the scheme is based on LWE problem, and it can resist quantum attacks, that is, CPA security under the standard model.