The geometric features of the keyhole directly reflect the quality of laser welding. However, predicting welding quality online has been a challenge in both engineering and academia due to the presence of chance and uncertainty. An innovative period-sensitive long short-term memory (PLSTM) neural network for predicting laser welding quality is proposed to address the dynamically changing characteristics of the keyhole. First, four key geometric features of the keyhole are extracted using an image preprocessing method. Second, the period factor in the sequence of geometric features of the keyhole is analyzed by Fourier transform and autocorrelation coefficient. Finally, a PLSTM neural network is established. Simulation results demonstrate that the proposed method exhibits stronger long term memory capability and temporal prediction capability compared to traditional methods. Furthermore, engineering experimental results indicate that the proposed method can be applied to the online prediction processes for laser welding quality.