This article considers the adaptive synchronization problem of delayed chaotic memristor-based neural networks (MNNs). Note that MNNs are modeled as continuous systems in the flux-voltage-time (ϕ,x,t) domain where memristors are viewed as continuous systems based on HP memristors. New adaptive controllers of MNNs are proposed, where controllers are both on memristors in the flux-time (ϕ,t) domain and neurons in the voltage-time (x,t) domain. Based on the Lyapunov method, Barbalat's lemma, differential mean value Theorem, and other inequality techniques, completed synchronization criteria for delayed chaotic MNNs are derived. In the end, two examples are given to demonstrate the validity of the derived results.