We present an efficient incremental topdown parsing method for preordering based on Bracketing Transduction Grammar (BTG). The BTG-based preordering framework (Neubig et al., 2012) can be applied to any language using only parallel text, but has the problem of computational efficiency. Our top-down parsing algorithm allows us to use the early update technique easily for the latent variable structured Perceptron algorithm with beam search, and solves the problem. Experimental results showed that the topdown method is more than 10 times faster than a method using the CYK algorithm. A phrase-based machine translation system with the top-down method had statistically significantly higher BLEU scores for 7 language pairs without relying on supervised syntactic parsers, compared to baseline systems using existing preordering methods.