Abstract: Chaos phenomenon of sampling phase-detector digital synthesizer loop is studied. First, the systems of sampling phase-detector digital synthesizer loop is discretization handled and the discretization systems model is given. In this systems, loop filter is RC integral filter and phase-detector is triangle phase-detector characteristic. By verifing the corresponding lower dimension system of discretization systems has the Snapnack Repeller, it is proof that original system output chaos when certain conditions of system parameters are satisfied. The relation between chaos and the parameter of the system is given finally.