A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by inline image, is the minimum cardinality of an independent dominating set. In this article, we show that if inline image is a connected cubic graph of order n that does not have a subgraph isomorphic to K2, 3, then inline image. As a consequence of our main result, we deduce Reed's important result [Combin Probab Comput 5 (1996), 277–295] that if G is a cubic graph of order n, then inline image, where inline image denotes the domination number of G.