Weak signal detection is a vital technology in underwater acoustic communication with strong noise background. In this area, non-autonomous Duffing system is still widely used, and a lot of researches focus on enhancing the ability to detect weak signal and to find out the detection limitation of the Duffing system. Moreover, great achievements have already made. But problems still exist such as non-convergence of the periodic state of the Duffing system and its narrow detection domain. Unfortunately, researches on weak signal detection by using other systems are still rare. In order to solve the above problems, a new three-dimensional similar Liu chaotic system for weak signal detection is proposed. A thorough theoretical analysis for the similar Liu chaotic system is given, and its equilibrium point and the Lyapunov index are deduced and analyzed in detail. The major conclusion is that the variable x of the new system becomes a deformation signal when the input signal amplitude is greater than a certain critical value, the variables y and z converge to zero, and the Lyapunov exponents are less than zero at the same time. This means that no matter how strong the input signal is, the detection can be achieved by using a similar Liu chaotic system as long as its amplitude exceeds the threshold value. The periodic convergence and wide area detection of the similar Liu chaotic system are proved by the Matlab simulation, the Multisim circuit simulation, and the actual circuit test. This new system solves the two problems of the period convergence and narrow detection domain for the traditional Duffing system. The periodic state and chaotic state are easy to distinguish when detected. The periodic state can be maintained when the signal amplitude changes from short distance to long distance in a new system. The spectral signal-to-noise ratio range increases up to -46:57 dB in the similar Liu chaotic system. The characteristics of the new system are only effected by its structure and parameters. The system does not rely on the external factors, and it can be extended. By using some switching devices, the conversion between the chaotic state and periodic state can be realized in the practical engineering applications with a higher detection accuracy. The new design concept of the similar Liu chaotic system shows a very high practical value. It will lay a certain foundation for the underwater acoustic communication of the ocean internet of things in the future.