Digital IIR notch filter has been employed in various communication systems to eliminated unwanted narrowband interference with known frequency. In this paper, the optimal multiple notch filter design is proposed based on the pole re-position technique. The optimality considered is based on the minimization of resulting filter magnitude response from the ideal notch magnitude response, measured in term of numerical sum of error square. Furthermore, by using Grobner basis, the symbolic solution and design method can be generalized to the higher number of notch frequencies case. The design algorithm can be implemented directly on Matlab platform and optimal filter coefficients can be found via numerical optimization/search. The advantage of the proposed algorithm is that the designer can specify additional performance parameters such as stability margin (distant from largest pole to the nearest point on the unit circle), maximum passband gain and quality factor.