Fog-based MANET (Mobile Ad hoc networks) is a novel paradigm of a mobile ad hoc network with the advantages of both mobility and fog computing. Meanwhile, as traditional routing protocol, ad hoc on-demand distance vector (AODV) routing protocol has been applied widely in fog-based MANET. Currently, how to improve the transmission performance and enhance security are the two major aspects in AODV's research field. However, the researches on joint energy efficiency and security seem to be seldom considered. In this paper, we propose a source anonymity-based lightweight secure AODV (SAL-SAODV) routing protocol to meet the above requirements. In SAL-SAODV protocol, source anonymous and secure transmitting schemes are proposed and applied. The scheme involves the following three parts: the source anonymity algorithm is employed to achieve the source node, without being tracked and located; the improved secure scheme based on the polynomial of CRC-4 is applied to substitute the RSA digital signature of SAODV and guarantee the data integrity, in addition to reducing the computation and energy consumption; the random delayed transmitting scheme (RDTM) is implemented to separate the check code and transmitted data, and achieve tamper-proof results. The simulation results show that the comprehensive performance of the proposed SAL-SAODV is a trade-off of the transmission performance, energy efficiency, and security, and better than AODV and SAODV.