<p>Matrix completion is often expressed as a low-rank matrix approximation problem that aims to recover missing entries from a finite set of elements observed in the whole matrix. Traditional methods approximate the rank function by minimising the nuclear norm, in which the singular values are minimised simultaneously, thus the approximation of the rank function is not effective and the robustness of matrix completion optimisation model is poor. Then the truncated nuclear norm regularization (TNNR) method is proposed, which approximates the rank function more accurately, but TNNR is not robust to the number of singular values and the iterative convergence is slow. Thus this paper proposes a revised weighting method based on the weighted residual TNNR, which assigns different weights to the rows of a matrix and weighs the priority of other rows in the neighbourhood range, then we retain the initial Frobenious-norm constraint as an error function and add an impact factor, named FW-TNNR, which further accelerates the iterative convergence and improves the performance of TNNR. Instead of the iterative updating scheme in the second step of TNNR, this paper provides a robust estimation and an effective strategy for the gradient descent approach with theoretical guarantees. The experimental results show that FW-TNNR has better recovery performance in the optimization process and is more robust to the truncated singular value <i>r</i>.</p>