With the accumulation of data generated by biological experimental instruments, using hierarchical multi-label classification (HMC) methods to process these data for gene function prediction has become very important. As the structure of the widely used Gene Ontology (GO) annotation is the directed acyclic graph (DAG), GO based gene function prediction can be changed to the HMC problem for the DAG of GO. Due to HMC, algorithms for tree ontology are not applicable to DAG, and the accuracy of these algorithms is low. Therefore, existing algorithms cannot satisfy the requirements of gene function prediction. To solve this problem, this paper proposes a DAG hierarchical multi-label classification algorithm, C2AE-DAGLabel algorithm. The C2AE-DAGLabel algorithm uses the Canonical Correlated AutoEncoder (C2AE) model as the classifier and designs a DAGLabel algorithm to solve the DAG hierarchical constraint problem. The DAGLabel algorithm can improve the classification accuracy by ensuring that the classification results meet the requirements of the hierarchical constraint. In the experiment, human gene data annotated with GO are used to evaluate the performance of the proposed algorithm. The experimental results show that compared with other state-of-the-art algorithms, the C2AE-DAGLabel algorithm has the best performance in solving the hierarchical multi-label classification problem for DAG.