We present a Minimum Bayes Risk (MBR) decoder for statistical machine translation. The approach aims to minimize the expected loss of translation errors with regard to the BLEU score. We show that MBR decoding on N-best lists leads to an improvement of translation quality. We report the performance of the MBR decoder on four different tasks: the TCSTAR EPPS Spanish-English task 2006, the NIST Chinese-English task 2005 and the GALE Arabic-English and Chinese-English task 2006. The absolute improvement of the BLEU score is between 0.2% for the TC