In this paper, we propose a new class of graphs called generalized recursive circulant graphs which is an extension of recursive circulant graphs. While retaining attractive properties of recursive circulant graphs, the new class of graphs achieve more flexibility in varying the number of vertices. Some network properties of recursive circulant graphs, like degree, connectivity and diameter, are adapted to the new graph class with more concise expression. In particular, we use a multidimensional vertex labeling scheme in generalized recursive circulant graphs. Based on the labeling scheme, a shortest path routing algorithm for the graph class is proposed. The correctness of the routing algorithm is also proved in this paper.