Abstract: The algorithm applied to glue all those trimmed free surfaces in a model, is one of the sub-algorithm in the transfer from initial CAD model to “watertight” mesh model. In this paper, the structure of initial multiple trimmed surfaces is described firstly, then the data structure in the algorithm is introduced. At last, the algorithm in detail implementation is provided. By using the algorithm, we can not only stitch multiple trimmed surfaces but also repair those initial CAD defects such as gap, overlap as well as the poor parameter curves such as degeneracy, folding, and self intersecting. Test results indicate the stability and efficiency of the algorithm. Two examples and their relative data are attached at the end of the paper.