This paper proposes a recognition system of constrained handwritten Hangul and alphanumeric characters using discrete hidden Markov models (HMM). HMM process encodes the distortion and similarity among patterns of a class through a doubly stochastic approach. Characterizing the statistical properties of characters using selected features, a recognition system can be implemented by absorbing possible variations in the form. Hangul shapes are classified into six types by fuzzy inference, and their recognition is performed based on quantized features by optimally ordering features according to their effectiveness in each class. The constrained alphanumerics recognition is also performed using the same features used in Hangul recognition. The forward-backward, Viterbi, and Baum-Welch reestimation algorithms are used for training and recognition of handwritten Hangul and alphanumeric characters. Simulation result shows that the proposed method recognizes handwritten Korean characters and alphanumerics effectively.