Abstract: Using the method of infinitesimal transformations, a new invariance of the generalized Hamilton system under infinitesimal transformations of time and coordinates is studied. From this the conditions and forms of existence of a conserved quantity of the system are derived. A new method to seek the conserved quantity is given. Some typical examples are given to illustrate the application of the method. The results indicate that the method is different from the Noether method, the Lie method and the form invariance method.