The motion of constrained system may be described in terms of non-independent state functions. We considered the change of the action integral and constraint equations under the infinitesimal transformation of the time-space points and state functions of the constrained system, this leads to the general transformation result. We obtained the general equations for the transformation properties of constrained system along the trajectory of motion of that system. From these equations, the condition under which the transformation of constrained system yields conservation law can be worked out. For some specific transformations of the continuous system, we have found the equations of transformation properties. In the special cases, the general equations of transformation properties can be reduced to the results the classical Noether's theorem, The application of general results to classical mechanics is discussed in detail and the Poincare-Cartan invariant is generalized to the constrained system.