The Kerr nonlinearity behavior in an Er3+-doped ZrF4–BaF2–LaF3–AlF3–NaF optical fiber is investigated theoretically. It is found that by increasing the intensity of the coherent coupling field and in the presence of an incoherent pumping field, the enhanced Kerr nonlinearity with reduced absorption can be achieved at long wavelength, i.e. λ = 1550 nm, which is practical for communicational applications. In addition, it is found that the rate of incoherent pump field can significantly decrease the maximal Kerr nonlinearity of the medium. The impact of frequency detuning of the coherent field on linear and nonlinear susceptibilities is discussed.