Recently, there has been a growing interest in chaotic memristive circuits. However, four-dimensional (4D) memristive system often can only exhibit common chaos with only one positive Lyapunov exponent. By replacing the resistor of Chua’s circuit with a memristor, we propose a new simple 4D memristive circuit in this paper. A major difference between our proposed system and the known chaotic or hyperchaotic system is that our modified system has infinitely many stable and unstable equilibria. We show that the system can exhibit rich complex dynamic behaviors, such as limit cycles, chaos and hyperchaos. Further numerical study and circuit simulation verify the existence of a hyperchaotic attractor in the memristive circuit, which gives a positive answer about whether there exists hyperchaos in 4D memristive systems.