Doppler broadening of positron annihilation spectroscopy was performed during high-power short-pulsed laser irradiation to investigate the effects of the induced shock waves on the measured positron annihilation parameters of Cu and W. The measurements were performed using the recently developed technique of accelerator-based γ-ray induced positron annihilation spectroscopy. The Doppler broadening was measured in coincidence with nanosecond laser pulses. Preliminary results show no significant effects in these measurements. These experiments have, however, demonstrated the potential of measuring positron annihilation spectra in coincidence with shock waves.