This paper characterizes laser-generated guided waves in a metal-lined composite-overwrapped pressure vessel (COPV) to assess typical damage, including interfacial debonding and low-velocity impact damage. First, an eigenfrequency approach that avoids additional coding is utilized to theoretically analyze the dispersion characteristics of a COPV. The theoretical results show that interfacial debonding significantly alters dispersion curves, and the wavenumber of the L(0, 1) mode is sensitive to impact damage. Experimental verifications were conducted based on the full wavefield acquired using a scanning laser-ultrasonic system with a repetition rate of 1 kHz. By comparing the experimental dispersion curves with the theoretical ones, it was found that the metal-composite interface was not bonded. In addition, a local wavenumber estimation method was established to detect the impact damage by obtaining the spatial distribution of the wavenumber of the L(0, 1) mode.