In the present investigation, a series of some novel 1,3-diaryl/heteroarylprop-2-en-1-one derivatives (3a-j) have been synthesized and evaluated for their in vitro cytotoxicity against three cancer cell lines, two hepatocarcinoma cell lines HUH-7, Hep-3b and one leukemia cancer cell line MOLT-4. Based on these results, structure-activity relationship (SAR) was studied on modification of $R^1$ and $R^2$ to identify the compound with maximum potency. Amongst the compounds, 3b and 3d strongly inhibited the growth of Hep-3b and MOLT-4 cells with $IC_{50}$ value of 3.39 and $3.63{mu}M$ respectively. The results obtained from the inhibitory study had further been supported by the reactive oxygen species (ROS) measurement using flow cytometry in MOLT-4 cells. These observations collectively reveal that compounds comprising 1,3-diarylprop-2-en-1-one framework with pyrazole ring at position-3 and heteroaryl/aryl substituents at position-1 can be used as promising anticancer agents.