Majorana fermions have attracted a great deal of attention in part due to their potential application in quantum computation.One decade ago Kitaev proposed a basic theoretical model to exhibit Majorana fermions.A quantum wire lies on the surface of a p-wave superconductor, it supports two isolated Majorana fermions at the ends of the wire.Recently, numerical calculations for Majorana zero modes of this model in two special cases have been performed using a method named Bogoliubov de Gennes diagonalization.