The augmented Lü system is a three-dimensional chaotic system, which can generate a false 4-wing attractor with only two control parameters. By using the method of anti-control chaos, a new three-dimensional chaotic system, named as generalized augmented Lü system, is proposed by the introducing a simple linear state controller into the augmented Lü system. The new system implements a real 4-wing attractor with compound structure and contains two mirrored symmetrical sub-system. By either of theoretical analyses, numerical simulations and circuit experiments, the existence of 4-wing chaotic attractor evolved from the generalized augmented Lü system is verified. It is also elaborated that the generalized augmented Lü system having more abundant dynamical behaviors than the augmented Lü system.