BRD4 (bromodomain-containing protein 4) is an epigenetic reader that realizes histone proteins and promotes the transcription of genes linked to cancer progression and non-cancer diseases such as acute heart failure and severe inflammation. The highly conserved N-terminal bromodomain (BD1) recognizes acylated lysine residues to organize the expression of genes. As such, BD1 is essential for disrupting BRD4 interactions and is a promising target for cancer treatment. To identify new BD1 inhibitors, a SuperDRUG2 database that contains more than 4600 pharmaceutical compounds was screened using in silico techniques. The efficiency of the AutoDock Vina1.1.2 software to anticipate inhibitor-BRD4-BD1 binding poses was first evaluated based on the co-crystallized R6S ligand in complex with BRD4-BD1. From database screening, the most promising BRD4-BD1 inhibitors were subsequently submitted to molecular dynamics (MD) simulations integrated with an MM-GBSA approach. MM-GBSA computations indicated promising BD1 binding with a benzonaphthyridine derivative, pyronaridine (SD003509), with an energy prediction (ΔGbinding) of −42.7 kcal/mol in comparison with −41.5 kcal/mol for a positive control inhibitor (R6S). Pharmacokinetic properties predicted oral bioavailability for both ligands, while post-dynamic analyses of the BRD4-BD1 binding pocket demonstrated greater stability for pyronaridine. These results confirm that in silico studies can provide insight into novel protein–ligand regulators, specifically that pyronaridine is a potential cancer drug candidate.