The present paper proposes a new probabilisticneural network (NN) that can estimate a posteriori probabilityfor a pattern classification problem. The structure of the proposednetwork is based on a statistical model composed by a mixtureof log-linearized Gaussian components. However, the forwardcalculation and the backward learning rule can be defined in thesame manner as the error backpropagation NN. In this paper, theproposed network is applied to the electroencephalogram (EEG)pattern classification problem. In the experiments, two types of aphotic stimulation, which are caused by eye opening/closing andartificial light, are used to collect the data to be classified. It isshown that the EEG signals can be classified successfully andthat the classification rates change depending on the number oftraining data and the dimension of the feature vectors.