This paper proposes a new memristor model and uses pinched hysteresis loops (PHL) to prove the memristor characteristics of the model. Then, a new 6D fractional-order memristive Hopfield neural network (6D-FMHNN) is presented by using this memristor to simulate the induced current, and the bifurcation characteristics and coexistence attractor characteristics of fractional memristor Hopfield neural network is studied. Because this 6D-FMHNN has chaotic characteristics, we also use this 6D-FMHNN to generate a random number and apply it to the field of image encryption. We make a series of analysis on the randomness of random numbers and the security of image encryption, and prove that the encryption algorithm using this 6D-FMHNN is safe and sensitive to the key.