Shi et al. \cite{shi2022understanding} propose acceleration methods to solve smooth convex optimization problems. In our work, we focus on the general unconstrained composite non-smooth convex optimization problem. We provide an inertial forward-backward algorithm with subgradient correction, derived through time discretization of the ODE, as studied by Shi et al. We achieve the rate of convergence of the objective gap as O(1⁄t²) and the o(1⁄t³) rate of convergence of the squared subdifferential norm for α ≥ 3. When α>3, the rate of objective gap is improved to o(1⁄t²), and also the iterative sequence generated by the algorithm converges to a minimal point. Furthermore, we analyze the inexact version of the proposed algorithm. The effectiveness of the proposed method has been demonstrated through various numerical studies.