With the continuous advancement of shale oil exploration and development, well logging data has become increasingly important in reservoir evaluation. However, due to factors such as logging equipment failures and cost constraints, missing or abnormal well log curves frequently occur, which severely impact the accuracy of geological interpretation and resource development. To address the issues of missing and abnormal well log curves, a deep learning model termed Inception-BiGRU-Transformer (IBT) is proposed by integrating a Transformer encoder to enhance global feature representation, a bidirectional gated recurrent unit (BiGRU) for temporal modeling, and an Inception module for multi-scale feature extraction. This model effectively improves the reconstruction accuracy and stability of well log curves through its combined multi-scale feature extraction and sequential modeling mechanisms. Experiments are conducted on measured data from twelve wells in the Daqing Gulong shale oil region, involving both single-target and multi-target well log curve reconstruction tasks. The results demonstrate that the IBT model outperforms mainstream models in terms of RMSE, MAE, MAPE, and R², exhibiting superior predictive accuracy and generalization capability. Furthermore, ablation studies confirm the effectiveness of each component in enhancing the model’s predictive performance.