A Viterbi decoder includes: an observation vector sequence generator for generating an observation vector sequence by converting an input speech to a sequence of observation vectors; a local optimal state calculator for obtaining a partial state sequence having a maximum similarity up to a current observation vector as an optimal state; an observation probability calculator for obtaining, as a current observation probability, a probability for observing the current observation vector in the optimal state; a buffer for storing therein a specific number of previous observation probabilities; a non-linear filter for calculating a filtered probability by using the previous observation probabilities stored in the buffer and the current observation probability; and a maximum likelihood calculator for calculating a partial maximum likelihood by using the filtered probability. The filtered probability may be a maximum value, a mean value or a median value of the previous observation probabilities and the current observation probability.