In　this　paper　a　simple　infinity　norm　based　neural　network　algorithm　for　estimation　of　the　principal　component　is　developed.　It　seems　to　be　especially　useful　in　applications　with　changing　environment,　where　the　learning　process　has　to　be　repeated　in　on-line　manner.　Theoretical　analysis　shows　the　weight　vector　converges　to　the　principal　eigenvector　asymptotically.　In　comparison　with　the　existing　algorithms,　numerical　simulation　shows　that　the　proposed　algorithm　demonstrates　fast　convergence　and　robustness　for　a　slightly　noisy　Gaussian　samples　with　some　points　having　large　magnitude　and　angle　with　respect　to　the　principal　direction.