In this paper, a new design method for digital infinite impulse response (IIR) filters with nearly linear-phase response is presented using fractional derivative constraints (FDCs). In the proposed method, design problem of an IIR filter is constructed as the minimization of phase error between the desired and de-signed phase response of an allpass filter (APF) such that the de-signed lowpass filter (LPF) or highpass filter (HPF) yields less passband (ep), and stopband errors (es) with optimal stopband at-tenuation (As). In order to have accurate passband (pb) response, FDCs are imposed on appropriate reference frequency, where the optimality of these FDCs are ensured by using a new greedy based sorting mechanism. The simulated results reflect the effi-ciency of the proposed method in term of improved passband re-sponse along with better transition width. However, small reduc-tion in As is observed within the allowable limit, when compared to non-fractional design approach, but the designed filter re-mains immune to wordlength (WL) effect.