In this paper we construct massive supermultiplets out of appropriate set of massless ones in the same way as massive spin s particle could be constructed out of massless spin s, s−1, ones leading to gauge invariant description of massive particle. Mainly we consider massive spin 3/2 supermultiplets in a flat d = 4 Minkowski space both without central charge for N = 1, 2, 3 as well as with central charge for N = 2, 4. Besides, we give two examples of massive N = 1 supermultiplets with spin 3/2 and 2 in AdS₄ space.