In order to solve the problem of group delay of filter design, this paper presents pre-distorted design method with Bessel function for coupled resonator filter and multiplexer with the maximally flat group delay characteristic. At the same time, the formulas and unitary parameter table of Bessel function has been gotten in this paper. The directly coupled resonator pass band filter and multiplexer can be achieved by using this approach. The design two examples are presented and the group delay is flat. The results validate its effectiveness.