This paper proposes features based on parametric representation of Fourier phase of speech for speaker verification. Direct computation of Fourier phase suffers from phase wrapping, and hence we attempt parametric modelling of phase spectrum using an allpass (AP) filter. The coefficients of the AP filter are estimated by minimizing an entropy based objective function motivated from speech production process. The AP cepstral coefficients (APCC) derived from the group delay response of estimated AP filter are used as features for speaker verification. An i-vector based speaker verification system is employed to evaluate the performance of the proposed APCC features on NIST 2003 speaker recognition evaluation database. The speaker verification system built using APCC features delivered an equal error rate (EER) of 7.58%, illustrating the speaker-specific nature of phase spectrum. The baseline speaker verification system built on mel-frequency cepstral coefficients (MFCC) gave an EER of 1.32%. A relative improvement of 12% was obtained over MFCC features by combining evidences from both MFCC and APCC based systems.