Cancers present a significant medical problem despite the development of medical and pharmaceutical sciences leading to a search for further therapeutic approaches. One such approach could involve the use of curcumin or its derivatives. Curcumin reveals interesting antineoplastic effects that could help in the treatment of cancer diseases. However, this natural product possesses some limitations which prevent its application in medicine. Among its limitations, it is characterized by poor water solubility, low stability, and unsatisfactory bioavailability. Aiming to improve the pharmacokinetic properties and enhance the biological effects of curcumin, a series of 30 chemical compounds inspired by its structure was synthesized and characterized. New compounds were subjected to a preliminary MTT viability assessment of 5637 and SCaBER bladder cancer cell lines. Some derivatives revealed the cytotoxic activities already at the concentration of 1 µM. The most active compounds showed no significant acute toxicity in the Microtox test. Intracellular uptake on the basis of the fluorescent properties of the new compounds was analyzed. It was also found that the presence of the morpholine group in the structure improved the biological activity of studied curcumin derivatives. As selected compounds could be considered potential drug candidates, further studies are necessary towards recognition of the exact mechanism of cellular action, the in vivo stability, and toxicity.