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An explicit inverse model of a magnetorheological (MR) damper is established to track the desired force in real time through experimental analysis and mathematical modeling. An algebraic hyperbolic tangent model is used to present the nonlinear behavior of MR dampers to avoid dynamic evolution due to effortless invertibility. A characteristic method is utilized to obtain the initial parameters of this algebraic hyperbolic tangent model; subsequently, the main parameters of the algebraic model are selected as quadratic functions of the applied current such that the closed-form expressions of the inverse model can be obtained. Then, the response time including communication and electromagnetic interactions in the experiment is investigated and modeled. By combining the force-current and electromagnetic models, an inverse model-based force tracking scheme is proposed. A series of validated tests are performed to study the force tracking performance. The proposed model exhibits high fidelity for tracking variable desired forces in experiments. Further analysis on force tracking errors demonstrates the mitigation of errors in various current fluctuating methods.