Nucleic acid-binding proteins play roles in many biological processes and cellular functions, such as replication, transcription, translation, RNA splicing, and methylation. Recently, many machine-learning models have been proposed to identify potential DNA-binding or RNA-binding residues from primary amino acid sequences. However, many nucleic acid-binding proteins are likely to be characterized by non-canonical binding elements. In this study, we questioned whether the affinity profiles of DNA-binding (DBPs) or RNA-binding (RBPs) proteins can be predicted by the multi-omics data including also the primary protein sequences. To this end, we collected experimentally annotated 1,447 DBPs and 351 RBPs. Using selected 555 and 374 multi-omics molecular features including primary amino acid profiles, proteins domains, post-translational modifications, solvent accessibility, secondary structures, tissue specificity index, and protein abundance level, we built two random forest classifiers and two SVM classifiers to predict DBPs and RBPs and achieved the AUC scores of 0.834 and 0.804 for the DBP model and 0.911 and 0.91 for the RBP model respectively, with 10-fold cross-validation. Intriguingly, the top-ranked important features with the best prediction performance are mostly non-domain-specific. This result suggests that protein domains are not the main contributors to identifying DBPs or RBPs, and we propose multi-omics molecular features to be a useful identifier to detect novel DBPs and RBPs with our machine-learning models.