In this study, a commercial agent with antivirus activity and moroxydine hydrochloride were employed to perform a lead optimization. A series of 1,3,5-triazine derivatives with piperazine structures were devised and synthesized, and an evaluation of their anti-potato virus Y (PVY) activity revealed that several of the target compounds possessed potent anti-PVY activity. The synthesis of compoundC35was directed by a 3D-quantitative structure–activity relationship that used the compound’s structural parameters. The assessment of the anti-PVY activity of compoundC35revealed that its curative, protective, and inactivation activities (53.3 ± 2.5%, 56.9 ± 1.5%, and 85.8 ± 4.4%, respectively) were comparable to the positive control of ningnanmycin (49.1 ± 2.4%, 50.7 ± 4.1%, and 82.3 ± 6.4%) and were superior to moroxydine hydrochloride (36.7 ± 2.7%, 31.4 ± 2.0%, and 57.1 ± 1.8%). In addition, molecular docking demonstrated thatC35can form hydrogen bonds with glutamic acid at position 150 (GLU 150) of PVY CP, providing a partial theoretical basis for the antiviral activity of the target compounds.