Laser ultrasonic detection technology is used in the field of additive manufacturing to quantitatively identify surface cracks in metal additive parts. However, the laser ultrasonic signal has serious multi-mode mixing, a complex waveform, and a low signal-to-noise ratio. An empirical wavelet transform technique is proposed to decompose the laser ultrasonic signal and use the difference between the peaks and troughs of the defect echoes of surface waves to quantitatively identify surface cracks in metal additive parts. The time-frequency characteristics of a laser ultrasonic signal were analyzed, and its surface wave modes were decomposed and adaptively extracted using an empirical wavelet transform. The differences between the peaks and troughs of the original signal and a surface wave signal extracted using the empirical wavelet transform were analyzed in the time range with or without a crack reflected echo. Then, the scanning position-differences between the peaks and troughs of the original signal and the surface wave signal were determined. The comparison showed that the latter could better determine the starting and ending positions of a crack. The absolute error of the crack detection results was less than 0.4 mm, and the relative error was less than 6.00%. This method was effective and feasible for feature extraction and the quantitative identification of laser ultrasonic signals, and it provides a powerful tool for the non-contact detection of surface crack defects in metal additive parts produced in a complex additive manufacturing environment.