Due to their biological interpretability, memristors are widely used to simulate synapses between artificial neural networks. As a type of neural network whose dynamic behavior can be explained, the coupling of resonant tunneling diode-based cellular neural networks (RTD-CNNs) with memristors has rarely been reported in the literature. Therefore, this paper designs a coupled RTD-CNN model with memristors (RTD-MCNN), investigating and analyzing the dynamic behavior of the RTD-MCNN. Based on this model, a simple encryption scheme for the protection of digital images in police forensic applications is proposed. The results show that the RTD-MCNN can have two positive Lyapunov exponents, and its output is influenced by the initial values, exhibiting multistability. Furthermore, a set of amplitudes in its output sequence is affected by the internal parameters of the memristor, leading to nonlinear variations. Undoubtedly, the rich dynamic behaviors described above make the RTD-MCNN highly suitable for the design of chaos-based encryption schemes in the field of privacy protection. Encryption tests and security analyses validate the effectiveness of this scheme.