Inelastic Compton scattering of photons by hydrogenic ions in a classical nonideal plasma is investigated. An effective pseudopotential model taking into account plasma screening and collective effects is applied to describe the interaction potential in a nonideal plasma. The screened atomic wave functions and energy eigenvalues for the ground and excited states of the hydrogenic ion in a classical nonideal plasma obtained by the Ritz variational and perturbational methods. The expression for the lowest-order transition matrix element is obtained by a two-photon process associated with terms quadratic in the vector potential A. The inelastic Compton scattering cross-section horn the 1s ground state to the 2p excited state is obtained as a function of the incident photon energy, Debye length, and the non-ideality plasma parameter. It is found that the collective effect reduces the cross-section. The collective effect on the cross-section is decreased with increasing Debye length.