Bromodomains (BRDs) are key transcriptional regulators that control expression of genes. Dysfunction of BRDs has been associated with the development of aggressive tumors. BRDs have emerged as attractive candidates for the development of inhibitors targeting gene transcription. Flavones can act as a potent anticancer agent. In this paper, a series of ten new flavonylquinazoline sulfonamide compounds (FQ1‐FQ10) was synthesized and their cytotoxicity was investigated in human A549 lung carcinoma, MCF‐7 breast carcinoma ve K562 myeloid leukemia cell lines. The most cytotoxic compounds FQ1 and FQ6 were tested for their bromodomain containing 2 protein (BRD2), bromodomain containing 3 protein (BRD3) and bromodomain containing 4 protein (BRD4) inhibitor activities. The results showed that new FQ1 and FQ6 flavone compounds exhibited BRD2, BRD3 inhibitor activity. We suggest that flavonylquinazoline sulfonamide compounds have the potential to inhibit bromodomain activity, thus may be pharmacologically of interest for further investigations.