In this paper, a novel multitaper modified group delay function-based representation for speech signals is proposed. With a set of phoneme-based experiments, it is shown that the proposed method performs better that an existing multitaper magnitude (MT-MAG) estimation technique, in terms of variance and MSE, both in spectral- and cepstral-domains. In particular, the performance of MT-MOGDF is found to be the best with the Thomson tapers. Additionally, the utility of the MT-MOGDF technique is highlighted in a speaker recognition experimental setup, where an improvement of around $20\%$ compared to the next-best technique is obtained. Moreover, the computational requirements of the proposed technique is comparable to that of MT-MAG. The proposed feature can be used in for many speech-related applications; in particular, it is best suited among those that require information of speaker and speech.