The goal is to modify the known method of mirror descent (MD) in convex optimization, which having been proposed by A.S. Nemirovsky and D.B. Yudin in 1979 and generalized the standard gradient method. To start, the paper shows the idea of a new, so-called inertial MD method with the example of a deterministic optimization problem in continuous time. In particular, in the Euclidean case, the heavy ball method by B.T. Polyak is realized. It is noted that the new method does not use additional averaging of points. Then, a discrete algorithm of inertial MD is described. The proved theorem of the upper bound on error in objective function is formulated.