Well logs are the fundamental data for development and evaluation in the oil and gas field. In the actual exploitation process, missing or incomplete well logs are common due to borehole collapse and instrument failure. In this paper, a cascaded bidirectional long short-term memory network with residual attention is proposed to reconstruct well logs. Firstly, bidirectional long short-term memory (Bi-LSTM) is employed to extract the data features from the forward and backward direction of the missing well logs, considering the bi-directional correlation between the missing data and the context information with depth. Then, the residual structure and the attention mechanism are designed for Bi-LSTM network, named RA-Bi-LSTM, to obtain deeper semantic information of the long-sequence logging curve. Finally, we develop the cascaded RA-Bi-LSTM to solve the multiple logging curves reconstruction problems, where the synthetic logging curve obtained at each RA-Bi-LSTM module is combined with the known logging curves as new input to the next RA-Bi-LSTM module. Hence, unknown missing logging curves can be reconstructed by iterating the cascaded system. Extensive experiments and thorough analysis are validated on four wells in the Sulige gas field in China. Experimental results demonstrate the effectiveness and superiority of the proposed cascade structure on reconstruction accuracy.