A new series of non-carboxylic naproxen analogues, bearing a variety of ring systems, such as oxadiazoles 3a-c and 6a-c, cycloalkanes 4a-d, cyclic imides 5a-c, and triazoles 7-9 and 10a-c, was synthesized. In addition, in vitro antitumor activity and cyclooxygenase isozymes (COX-1/COX-2) inhibition assay of the target compounds 3-10 was studied. The results of the antitumor activity assays indicated that compounds 4b, 6c, 10b, and 10c exhibited the greatest antitumor activities against the tested cell lines MCF-7, MDA-231, HeLa, and HCT-116, with an IC50 range of 4.83-14.49 μM. By comparison, the reference drugs doxorubicin, afatinib, and celecoxib yielded IC50 values of 3.18-26.79, 6.20-11.40, and 22.79-42.74 μM, respectively. Furthermore, in vitro COX-1/COX-2 inhibition testing showed that the compounds 4b, 6c, 10b, and 10c exhibited effective COX-2 inhibition, with IC50 values of 0.40-1.20 μM, and selectivity index (SI) values of >62.50-20.83, using celecoxib as a reference drug (IC50 = 0.11 μM; COX-2 SI: >227.20). Compounds 6c and 10c, which were potent COX-2 inhibitors, were docked into the COX-2 binding site, where these compounds exhibited strong interactions.