Spin-fluctuation mechanism of superconductivity PuRhGa5 is considered in terms of the generalized Hubbard model for a system of strongly correlated d- and f-electrons. For the analysis of the instability to the superconducting state are made self-consistent calculations of electronic density of states and the magnetic susceptibility of the normal phase PuRhGa5. Found that the chemical potential is located in the immediate vicinity of the local maximum density of states of f-electrons. Is shown that the non-zero values of the superconducting order parameter has be for f-electrons and is associated with the presence of features (negative curvature) their density of states. The temperature dependence of the magnetic susceptibility and the value found for the transition temperature to the superconducting state agreement with the experimental data