In order to generate hyperchaotic signal, a class of hyperchaotic system circuits was realized by simply adding an integration circuit to a three-dimensional chaotic Lü system circuit. The hyperchaotic attractors along with chaotic, periodic and quasi-periodic attractors of these systems were obtained from circuit simulations. The corresponding continuous autonomous dissipative system equations were investigated theoretically and simulated numerically to verify the hyperchaotic and dynamical behaviors of the proposed hyperchaotic system circuits. The proposed hyperchaotic system circuits are easy to realize by adding only a few components, thus it may find practical applications.