A new type of conserved quantity which is directly induced by Mei symmetry of Hamilton system is studied. Firstly, the definition and criterion of Mei symmetry for Hamilton system are given. Secondly, a coordination function is introduced; the conditions from which the new type of conserved quantity can be induced by Mei symmetry and the form of the new type of conserved quantity are obtained. Lastly, an illustration example is given. The result indicates that the coordination function should be selected properly according to the demand of the gauge function, thereby the gauge function can be find out more easily. Furthermore, since the choice of the coordination function is not unique more conserved quantities of Mei symmetry for Hamilton system can be obtained.