A speech act is a linguistic action intended by a speaker. Speech act classification is an essential part of a dialogue understanding system because the speech act of an utterance is closely tied with the user's intention in the utterance. We propose a neural network model for Korean speech act classification. In addition, we propose a method that extracts morphological features from surface utterances and selects effective ones among the morphological features. Using the feature selection method, the proposed neural network can partially increase precision and decrease training time. In the experiment, the proposed neural network showed better results than other models using comparatively high-level linguistic features. Based on the experimental result, we believe that the proposed neural network model is suitable for real field applications because it is easy to expand the neural network model into other domains. Moreover, we found that neural networks can be useful in speech act classification if we can convert surface sentences into vectors with fixed dimensions by using an effective feature selection method.