Based on the acoustic elastic effect, the utilization of critical refracting longitudinal waves to detect the residual stress of metal materials has a wide application prospect. However, the critical refracting longitudinal wave velocity has a weak acoustic elastic effect on stress, which greatly affects the resolution of material stress detection. To improve the detection accuracy of the critical refracting longitudinal wave velocity, a nonlinear decomposition technique (wavelet synchrosqueezed transform) is proposed to transform and reconstruct the critical refracting longitudinal wave. In this way, the ultrasonic arrival time can be calculated accurately. Taking the 1 060 aluminum plate as the research object, the waveform features of critical refracting longitudinal wave are analyzed based on the finite element simulation software. Based on these features, the ultrasonic signals in the experiment are adjusted to improve the waveform accuracy of the critical refracting longitudinal wave. Experimental results show that the propagation time of the critically refracted longitudinal wave in the 1 060 aluminum plate can be accurately measured, and the wave velocity is calculated with an error of no more than 005%. The validity of the accurate calculation method of critical refracting longitudinal wave velocity is verified.