In Japanese dependency parsing, Kudo's relative preference-based method (Kudo and Matsumoto, 2005) outperforms both deterministic and probabilistic CKY-based parsing methods. In Kudo's method, for each dependent word (or chunk) a loglinear model estimates relative preference of all other candidate words (or chunks) for being as its head. This cannot be considered in the deterministic parsing methods. We propose an algorithm based on a tournament model, in which the relative preferences are directly modeled by one-onone games in a step-ladder tournament. In an evaluation experiment with Kyoto Text Corpus Version 4.0, the proposed method outperforms previous approaches, including the relative preference-based method.