We perform the quantization of a massive particle propagating on AdS(5). We use the twister formulation in which the action can be brought into a quadratic form. We construct the BRST operator which commutes with AdS(5) isometries forming SU(2,2). The condition of a consistent BRST quantization requires that the AdS energy E is quantized in units of the AdS, radius R, E = 1/2R(N-a + N-b + 4), With N-a, N-b being some non-negative integers. We also argue that the mass operator will be identified with the moduli of the U(1) central extension Z of the SU(2,2|4) algebra in the supersymmetric case. The spectrum of physical states with vanishing ghost number contains a particular subset of 'massless' SU(2,2) multiplets (including the bosonic part of the 'novel short' supermultiplets). We hope that our results will help to quantize also the string on AdS(5).