Novel sulfonamides 3–19 with a biologically active 3,4-dimethoxyphenyl moiety were designed and synthesized. The structures of the synthesized compounds were established using elemental analyses, IR, ¹H-NMR, ¹³C-NMR spectral data and mass spectroscopy. All the synthesized compounds were evaluated for their in vitro anticancer activity against four cancer cell lines, namely human hepatocellular carcinoma (HepG2), human medulloblastoma (Daoy), human cervical cancer (HeLa), and human colon cancer (HT-29), by using a 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay and dasatinib as the reference drug. Among the tested derivatives, compounds 4, 10, 16, and 19 showed good activity as cytotoxic agents. The most active derivatives were evaluated for their ability to inhibit vascular endothelial growth factor receptor (VEGFR)-2. Compounds Z-4-(3-(3,4-dimethoxyphenyl)-3-oxoprop-1-enylamino)-N-(5-methyl-1,3,4-thiadiazol-2-yl)-benzenesulfonamide 10 and Z-4-(3-(3,4-dimethoxyphenyl)-3-oxoprop-1-enylamino)-N-(1H-indazol-6-yl)-benzenesulfonamide 19 were more active as VEGFR-2 inhibitors than dasatinib. Molecular docking of the most active derivatives on the active site of VEGFR-2 revealed that compound 19 exhibited favorable and promising results.