The　traditional　k-means　algorithm　is　often　calculated　according　to　the　Euclidean　distance.　For　longitudinal　data　it　is　unable　to　perform　accurate　and　efficient　computing.　Based　on　extended　Frobenius-norm　(Efros)　distance,　in　this　study　we　proposed　a　method　to　improve　the　selection　of　initial　centers　for　k-means　clustering.　This　method　can　improve　the　traditional　k-means　clustering　on　longitudinal　data.　For　missing　longitudinal　data,　we　first　adopted　a　linear　interpolation　strategy　to　fill　in　missing　values　and　then　standardized　the　data,　etc.　Through　comprehensive　simulation　studies,　we　demonstrate　the　power　and　effectiveness　of　our　method　by　comparing　the　similarity　within　and　between　the　classes.　The　results　of　our　experiments　show　that　our　method　can　cluster　the　longitudinal　data　more　effectively.