This paper proposes a tree kernel method of semantic relation detection and classification (RDC) between named entities. It resolves two critical problems in previous tree kernel methods of RDC. First, a new tree kernel is presented to better capture the inherent structural information in a parse tree by enabling the standard convolution tree kernel with context-sensitiveness and approximate matching of sub-trees. Second, an enriched parse tree structure is proposed to well derive necessary structural information, e.g., proper latent annotations, from a parse tree. Evaluation on the ACE RDC corpora shows that both the new tree kernel and the enriched parse tree structure contribute significantly to RDC and our tree kernel method much outperforms the state-of-the-art ones.