In this paper, assuming that the score of a speech utterance is a weighted sum of hidden Markov model (HMM) log state-likelihoods, we propose a new method of finding discriminative state-weights recursively using the generalized probabilistic descent method. With this method the conventional parameter estimation method and the Viterbi algorithm can be applied to continuous speech recognition as well as isolated word recognition without large modification by constraining the sum of the state-weights to the number of states in a recognition unit. Compared with the previous approaches, this method does not increase complexity and can be implemented with minor modification of the conventional parameter estimation and recognition algorithms by constraining the sum of the state-weights to the number of states in a recognition unit, and further it can be applied to continuous speech recognition as well as isolated word recognition. To evaluate the performance of the state-weighted HMM recognizer, we perform two kinds of experiments with phoneme-based and word-based state-weights using various kinds of speech databases. Experimental results showed that the recognizers with phoneme-based and word-based state-weights achieved 20% and 50% decrease in word error rate, respectively, for isolated word recognition, and 5% decrease for continuous speech recognition. Our approach yields recognition accuracies comparable to those of the previous approaches for continuous speech recognition, but it is much simpler to implement than others.