In order to solve robust PageRank problem a saddle-point Mirror Descent algorithm for solving convex-concave optimization problems is enhanced and studied. The algorithm is based on two proxy functions, which use specificities of value sets to be optimized on (min-max search). In robust PageRank case the ones are entropy-like function and square of Euclidean norm. The saddle-point Mirror Descent algorithm application to robust PageRank leads to concrete complexity results, which are being discussed alongside with illustrative numerical example.