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In this study, a linearization method is used to develop an implicit integration scheme for a class of high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is first considered in which the inelastic strain rate is divided into transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The implicit integration scheme developed is shown to be applicable to a unified constitutive model in which back stress evolves due to static and dynamic recoveries in addition to strain hardening. The integration scheme is then programmed for a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is demonstrated that the integration scheme affords quadratic convergence in the iterations even for considerably large increments, and that the non-unified and unified models give almost the same results in the solder joint analysis.