Infection with strains of different subtypes and the subsequent crossover reading between the two strands of genomic RNAs by host cells' reverse transcriptase are the main causes of the vast HIV-1 sequence diversity. Such inter-subtype genomic recombinants can become circulating recombinant forms (CRFs) after widespread transmissions in a population. Complete prediction of all the subtype sources of a CRF strain is a complicated machine learning problem. It is also difficult to understand whether a strain is an emerging new subtype and if so, how to accurately identify the new components of the genetic source. We introduce a multi-label learning algorithm for the complete prediction of multiple sources of a CRF sequence as well as the prediction of its chronological number. The prediction is strengthened by a voting of various multi-label learning methods to avoid biased decisions. In our steps, frequency and position features of the sequences are both extracted to capture signature patterns of pure subtypes and CRFs. The method was applied to 7185 HIV-1 sequences, comprising 5530 pure subtype sequences and 1655 CRF sequences. Results have demonstrated that the method can achieve very high accuracy (reaching 99%) in the prediction of the complete set of labels of HIV-1 recombinant forms. A few wrong predictions are actually incomplete predictions, very close to the complete set of genuine labels. https://github.com/Runbin-tang/The-source-of-HIV-CRFs-prediction. Supplementary data are available at Bioinformatics online.