In this paper, we present a discriminative approach for reranking discourse trees generated by an existing probabilistic discourse parser. The reranker relies on tree kernels (TKs) to capture the global dependencies between discourse units in a tree. In particular, we design new computational structures of discourse trees, which combined with standard TKs, originate novel discourse TKs. The empirical evaluation shows that our reranker can improve the state-of-the-art sentence-level parsing accuracy from 79.77% to 82.15%, a relative error reduction of 11.8%, which in turn pushes the state-of-the-art documentlevel accuracy from 55.8% to 57.3%.