Time-delay chaotic systems with multiple positive Lyapunov exponents have been extensively studied in the field of information security. This paper proposes a new four-dimensional time-delay Lorenz system and its chaotic synchronization through the Lyapunov–Krasovskii theory. The sufficient conditions for the stability of the new chaotic system are obtained by the Routh–Hurwitz criterion, and the control parameters are found to have a significant impact on the speed of synchronous convergence. Furthermore, oscillation circuit simulation is essential for contributing the chaotic system to practical applications. Accordingly, the circuits of the chaotic time-delay system and its coupled synchronous control circuit are innovatively designed by Multisim. Experiment results illustrate the behaviors of various attractors in the new time-delay Lorenz system and the effectiveness of the proposed asymptotic synchronous method.