This paper considers the problem of merging grid maps that have different resolutions. Because the goal of map merging is to find the optimal transformation between two partially overlapping grid maps, it can be viewed as a special image registration issue. To address this special issue, the solution considers the non-common areas and designs an objective function based on the trimmed mean-square error (MSE). The trimmed and scaling iterative closest point (TsICP) algorithm is then proposed to solve this well-designed objective function. As the TsICP algorithm can be proven to be locally convergent in theory, a good initial transformation should be provided. Accordingly, scale-invariant feature transform (SIFT) features are extracted for the maps to be potentially merged, and the random sample consensus (RANSAC) algorithm is employed to find the geometrically consistent feature matches that are used to estimate the initial transformation for the TsICP algorithm. In addition, this paper presents the rules for the fusion of the grid maps based on the estimated transformation. Experimental results carried out with publicly available datasets illustrate the superior performance of this approach at merging grid maps with respect to robustness and accuracy.