Cognitive radio networks allow for online adaptation of system parameters to improve communication quality through sensing of the environment and learning from experience. CR networks which use orthogonal frequency division multiplexing as transmission technology at physical layer require the power resource to be allocated optimally. This optimal power resource allocation is performed subject to mutual interference constraint. Hence, this problem may be modeled as an optimization problem to arrive at the optimal power resource to be allocated. In this paper we utilize the accelerated gradient descent approach to allocate power to sub carriers in cognitive radio (CR) networks. The proposed accelerated gradient-based power allocation method can approximate the optimal solution within a few iterations. In this paper we have compared the proposed approach with the conventional gradient descent (GD) method which requires more number iterations for solving the power allocation problem. Further, the proposed accelerated gradient-based method and the gradient-based method both have a computational complexity of O (N<sup>2</sup>), but the proposed accelerated gradient-based method converges faster than the conventional approach. This paper presents both approaches and provides a comparative analysis of the proposed approach with the conventional approach.