In actual logging operations, various factors such ascomplex wellbore environment, complex geological structures, and wellbore collapses can lead to the issue of missing logging curves, and the cost of remeasuring data is high. To address the issue of missing logging curves, this paper first employs Singular Spectrum Analysis (SSA) to decompose the original logging curves, utilizing the more correlated components for more efficient curve completion. Furthermore, a logging curves completion model based on graph attention network incorporating Multi-Head Attention Mechanism and Bidirectional Gated Recurrent Units (GAT-MABiGRU) is proposed. In the completion experiments for the RHOB and DT logging curves, results show that the GAT-MABiGRU model based on SSA outperforms Support Vector Regression (SVR), Multi-Layer Perceptron (MLP), Long Short-Term Memory Network (LSTM), and Temporal Convolutional Network (TCN) in terms of Root Mean Squard Error(RMSE), Mean Absolute Error(MAE), and coefficient of determination(R²). Ablation experiments and blind well experiments further verify the effectiveness of incorporating SSA and GAT modules in improving the model's prediction accuracy, providing a new method for logging data completion.