We quantize a Brink-Schwarz superparticle in the AdS(5) x S-5 background with Ramond-Ramond(RR) flux from the first principle in the phase space formulation. It includes the construction of the quantum Noether charges for the psu(2, 2 vertical bar 4) superconformal symmetry and by solving the superconformal primary conditions we obtain the complete physical spectrum of the system with the explicit wave functions. The spectrum agrees precisely with the supergravity results, including all the Kaluza-Klein excitations.