In this paper, we present a new system of Duffing oscillator array to detect weak chirp signal utilizing the characteristics of chaotic system, which are the sensitivity to the initial condition and the immunity to the noise. Based on the Lyapunov Exponents (LE) calculated in the Wolf method, we can discriminate the output state of each oscillator in chaotic array quickly and accurately. Meanwhile, the system we proposed can detect the weak chirp signal using the property of the critical state and overcome the limitation of the previous research on chaotic system which can only be used in periodic signal detection. The contributions of this paper are as follows. On one side, we introduce a chaotic system to detect the weak chirp signal, which is the standard signal in radar communication, under ultra-low signal-to-noise ratio (SNR) effectively; On the other side, the previous research on chaotic system take the large-scale periodic state as the sign of whether the weak signal exist or not, while the proposed system in this paper utilizes the critical state's characteristics to estimate the frequency modulation rate (FMR) of the weak chirp signal novelly. Simulation results demonstrate that the proposed system can achieve a satisfactory performance in strong background noise with SNR low to -20dB, while traditional linear detection method does not work in the same condition.