Fog computing-enhanced IoT (Internet of Things), as it can provide better IoT services at the network edge, has received considerable attention in recent years. In this paper, for this new paradigm, we present a new privacy-preserving multi dot-product query scheme, called PMQ, which enables the control center to gain k dot-product results simultaneously in one query. Specifically, in the proposed PMQ scheme, the BGN homomorphic encryption is employed for encrypting query request and response, and a fog device is deployed at the network edge to assist the privacy-preserving k dot-product query. Detailed security analysis shows that the proposed PMQ can achieve better privacy preservation, i.e., no information in query request and response will be disclosed. In addition, extensive simulations are conducted, and the results demonstrate that the proposed PMQ scheme can achieve acceptable efficiency in terms of communication overheads and computational costs.