Distribution network data may encounter random missing data caused by abnormal conditions and continuous missing data caused by natural disasters during gathering, transmission, and conversion. To address these problems, this paper proposes a missing data imputation method based on the Temporal Generative Adversarial Network with Gradient Penalty (TGAN-GP), which takes the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) as its basic framework, replaces traditional fully connected layers with a Temporal Convolutional Network (TCN) in the generator’s core, leverages causal dilated convolution to efficiently capture the long-range temporal dependencies and periodicity of measurement data, and integrates residual connections to mitigate gradient vanishing and network degradation during deep training. For the discriminator, the method adopts a Long Short-Term Memory (LSTM) network, which enhances the evaluation of the temporal rationality of generated data and thereby further improves imputation accuracy. Finally, simulations were conducted on the IEEE 33-bus distribution network test system. Results show that under the random missing scenario (10% missing rate), the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) of node voltage magnitude imputation are as low as 0.00062 and 0.00051, those of node injected active power imputation are 0.00081 and 0.00065, and those of node injected reactive power imputation are 0.00082 and 0.00076. Under the continuous missing scenario, the RMSE and MAE of node voltage magnitude imputation are 0.00147 and 0.00122, those of node injected active power imputation are 0.00373 and 0.00268, and those of node injected reactive power imputation are 0.00314 and 0.00226. The imputation errors of all three data types are significantly lower than the comparison methods’.