A centroid type-reduction strategy for computing the centroids of type-2 fuzzy sets based on decomposed $\alpha$ -planes was proposed by Liu. However, it cannot be applied to type-2 fuzzy sets with concave secondary membership functions. In this paper, we extend the Liu's method so that the centroids of type-2 fuzzy sets with concave secondary membership functions can be derived. For each decomposed $\alpha$ -plane, we convert it into a group of interval type-2 fuzzy sets. The union of the centroids of its member interval type-2 fuzzy sets constitutes the centroid of the $\alpha$ -plane. Then, the weighted union of the centroids of the decomposed $\alpha$ -planes becomes the centroid type-reduced set of the original type-2 fuzzy set. When dealing with type-2 fuzzy sets with convex secondary membership functions, our proposed method is reduced to the Liu's method.