Part of speech tagging systems using neural networks have been proposed by Ma, et al. They can tag the untrained data at a practical level of accuracy by training a small Thai corpus with ten thousand order words. The multilayer perceptron (MLP) type of neural networks used, however, was found to converge slowly and took a very long time to train even the above mentioned small amount of training data. This paper presents an alternative method for solving the POS tagging problems with the min-max modular neural network proposed by Lu and Ito. By using this modular neural network, the part of speech tagging problems can be broken down into a number of independent smaller and simpler subproblems, and all of the subproblems can be learned by small network modules in parallel.