The Hamilton principle of intrinsical linear nonholonomic system was studied.The sufficient and necessary conditions of stationary for Hamilton variational function are given and proved by using Appell-Chetaev condition or not.The results show that the Hamilton's action variable is a stable one in instrinsical linear nonholonomic system and the Hamilton principle is similar to that of holonomic system.There are no mechanical or mathematical contradications in the equations of motion gotten from the Hamilton principle.Finally,the essential reasons are given why it is unconscionable for the Hamilton principle to be generalized to the intrinsical nonlinear nonholonomic system.