Based on Hilbert transform pairs of wavelet bases and stochastic resonance, a novel algorithm to detect underwater multipath acoustic transient signal is presented. Dual-tree complex wavelet transform with Hilbert transform pairs of wavelet bases is proposed to use as a solution to translation variance of DWT. Stochastic resonance is used to enhance the signal-to-noise ratio. The performance of the proposed algorithm is analyzed and four kinds of detectors are compared. It shows that dual-tree complex wavelet transform and stochastic resonance based detector has good performance far more than that of energy detector and than that of DWT, especially at low signal-to-noise ratio state.