Protein arginine methyltransferase 5 (PRMT5) is a popular anticancer target that regulates histone or nonhistone methylation and is linked to the development and poor prognosis of non-small cell lung cancer. PRMT5 inhibitors have shown great promise in clinical trials as a cancer therapy. However, most inhibitors reported recently act in a SAM-competitive mode and lack structural diversity. In this paper, a novel non-SAM inhibitor, 3039-0164, was discovered by the structure-based virtual screening method. The binding mechanism of 3039-0164 to PRMT5 was revealed via molecular docking and molecular dynamics simulations. 3039-0164 inhibited PRMT5 enzymatic activity, downregulated the expression of PRMT5 downstream target genes (FGFR3 and eIF4E), and blocked the activation of the PI3K/AKT/mTOR and ERK signaling pathways. The discovery of 3039-0164 provides precise and creative hit compounds for the design optimization of PRMT5 lead compounds in non-small cell lung cancer.