An anyon exciton formed by a valence hole and three quasielectrons of the Laughlin incompressible liquid of the fractional quantum Hall effect with the filling factor ν=1/3 is investigated numerically in a spherical geometry. The quasielectrons ar treated as Bose particles with hard cores and the Coulomb interaction. The energy spectrum of the system and the quasielectron density distribution around the hole are obtained. The energy spectrum of the system has branches which can be classified according to intrinsic angular momentum of an anyon exciton; the absence of branches with an angular momentum below three and a branch with an angular momentum equal to four is a consequence of the Pauli exclusion principle for quasielectrons.