This paper reports on a new application of the Markov model to an automatic speech recognition system, in which the feature vectors of speech are regarded to represent the states and the output symbols of the Markov model. The transition-probability of the states and the symbol-output probability are assumed to be represented by multidimensional normal density functions of the feature vector. The DP-matching algorithm is used for calculating optimum time sequence of observed feature vectors. In order to confirm the efficiency of this system, we compared experimentally performance of this system to that of other approaches, such as those using Maharanobis' distance or Euclidean distance. Based on experimentation, in a speaker independent mode, using a vocabulary of Japanese single-digit and four-digit numerals, the current system is shown to be more effective than others.