A four-dimensional interrelated and switchable Lü hyperchaotic system is built by adding an additional state into the three-dimensional Lü chaotic system. When subsystems are hyperchaotic，an identical system parameter is determined according to the bifurcation diagrams of these subsystems. Some of its basic dynamical properties are studied detailedly，such as the feature of equilibrium，the phase portraits of hyperchaotic attractor，the Lyapunov exponent and fractal dimension. A practical circuit is designed to realize these systems. Experimental result shows the effectiveness and feasibility of the theoretical analysis and verifies the behavior of various attractors.