The paper is devoted to designing an efficient recursive algorithm for solving the robust PageRank problem recently proposed by Juditsky and Polyak (2012). To this end, we reformulate the problem to a specific convex-concave saddle point problem $\min\nolimits_{x\in X} \max_{y \in Y} q(x, y)$ with simple convex sets $X\in\mathbb{R}^N$ and $Y\in\mathbb{R}^N$, i.e., standard simplex and Euclidean unit ball, respectively. Aiming this goal we develop an extension of saddle point mirror descent algorithm where additional parameter sequence is introduced, thus providing more degree of freedom and the refined error bounds. Detailed complexity results of this method applied to the robust PageRank problem are given and discussed. Numerical example illustrates the theoretical results proved.