This paper discusses a circular optical fiber consisting of an inhomogeneous nonlinear core bounded by a linear cladding medium. With such a fiber, the calculation of nonlinear modes is of practical importance because of the joint effects of nonlinearity and inhomogeneity in the field of concentration and optical confinement. The numerical results obtained indicate that the combination of this type of inhomogeneity and the characteristics of nonlinearity may play a significant role in optical confinement of the core.