Abstract <p>In the present paper, we have studied the nonrelativistic problem for a spin 3/2 particle in presence in the external Coulomb field. The known general procedure for performing the nonrelativistic approximation is based on the method of projective operators. This approach is applied directly in the relativistic system of radial equation derived previously for a free spin 3/2 particle for states with the spherical symmetry within the covariant tetrad formalism. The system of two 2-nd order differential equations describing the nonrelativistic particle has been derived. It refers to states with quantum numbers of energy, square and the third projection of the total angular momentum, and spatial parity. Solutions of radial equations have been constructed in terms of confluent hypergeometric functions, the corresponding energy spectra are found.</p>