This paper explores a tree kernel based method for semantic role labeling (SRL) of Chinese nominal predicates via a convolution tree kernel. In particular, a new parse tree representation structure, called dependency-driven constituent parse tree (D-CPT), is proposed to combine the advantages of both constituent and dependence parse trees. This is achieved by directly representing various kinds of dependency relations in a CPT-style structure, which employs dependency relation types instead of phrase labels in CPT (Constituent Parse Tree). In this way, D-CPT not only keeps the dependency relationship information in the dependency parse tree (DPT) structure but also retains the basic hierarchical structure of CPT style. Moreover, several schemes are designed to extract various kinds of necessary information, such as the shortest path between the nominal predicate and the argument candidate, the support verb of the nominal predicate and the head argument modified by the argument candidate, from D-CPT. This largely reduces the noisy information inherent in D-CPT. Finally, a convolution tree kernel is employed to compute the similarity between two parse trees. Besides, we also implement a feature-based method based on D-CPT. Evaluation on Chinese NomBank corpus shows that our tree kernel based method on D-CPT performs significantly better than other tree kernel-based ones and achieves comparable performance with the state-of-the-art feature-based ones. This indicates the effectiveness of the novel D-CPT structure in representing various kinds of dependency relations in a CPT-style structure and our tree kernel based method in exploring the novel D-CPT structure. This also illustrates that the kernel-based methods are competitive and they are complementary with the featurebased methods on SRL.