The decentralization and anonymity of blockchain have attracted significant attention. However, in recent years, there has been a rise in blockchain money laundering incidents, and anti-money laundering efforts have become crucial within the blockchain space. Blockchain money laundering differs from traditional financial money laundering as it does not provide account information, particularly in the case of Bitcoin. This absence of information makes it challenging for researchers to detect money laundering activities based on transaction data. We propose LB-GLAT, a novel Long-Term Bi-Graph Layer Attention Convolutional Network, to effectively capture the topological structure and attribute characteristics of money laundering on the blockchain transaction graph. LB-GLAT utilizes the transaction graph and the reverse transaction graph to solve the no-loop problem that results in the inability to capture the destination of blockchain transactions and designs a long-term layer attention mechanism to alleviate the over-smoothing problem. We implemented a series of experiments to evaluate LB-GLAT, which achieved state-of-art performance compared with other methods, presenting an accuracy of 0.9776, a precision of 0.9317, a recall of 0.8494, an F1−score of 0.8887, and an AUC of 0.9806.