In this paper, we propose three variants of Mann-type inertial forward–backward iterative methods for approximating the minimum-norm solution of the monotone inclusion problem and the fixed points of nonexpansive mappings. In the first two methods, we compute the Mann-type iteration together with the inertial extrapolation and fixed-point iteration in the initiation of the process, while the last method computes only the Mann-type iteration with inertial extrapolation at the start of the process. We establish the strong convergence results for each method with appropriate assumptions and discuss some applications of the presented methods. Finally, we present numerical examples in both finite- and infinite-dimensional Hilbert spaces to demonstrate their efficiency. A comparative analysis with existing methods is also provided.