Memristive chaotic oscillator has significant application value in multiple industrial fields. In this study, based on three piecewise linear functions and a new nonlinear memristor, we first develop a new extremely multistable grid-scroll memristive chaotic oscillator, and applied it to acoustic signal detection. The model can produce n × n × n-scroll attractor that extends infinitely along three dimensions, and all scroll attractors have the similar dynamic topology. These piecewise linear functions capable of producing regular sawtooth wave, breaking the internal balance of attractor and leading to random position switching. Specially, through controlling the parameter setting, we can obtain single- and multiscroll infinitely coexisting attractors in 3-D phase space, and a special spiral coexisting attractor is also discovered. The chaotic circuits of this oscillator model are achieved to verify its reproducibility and usability. Finally, combined with the 3 × 3-scroll oscillator, a novel underwater acoustic signal detection system is developed, capable of detecting periodic signal of each frequency. Compared with other oscillator models, our oscillator exhibits more obvious topological changes of attractors and greater immunity to noise. The minimum SNR for ship signals can reach −30 dB. The existence detection of ship signal verifies its feasibility in industrial applications.