Diagnosis of aphasia from electroencephalogram (EEG) was investigated. EEG data of the following patients were collected; the patient of total aphasia who is difficult to understand the speech and the patient of motor aphasia (Broca aphasia) who feels pain or makes some grammatical mistakes when he speaks anything while he can understand the speech. At first, power spectrum of EEG was extracted by the fast Fourier transform (FFT). The spectrum was separated into 9 regions, corresponding to the characterized wave. The regions with 4.0 to 5.9, 6.0 to 7.9 and 8.0 to 12.9 Hz were selected as the frequency band of θ1, θ2, and α waves, respectively. Assessment of linguistic ability was carried out by Western aphasia battery (WAB). The relative power values were input into each NN model for estimation of aphasia quotient (AQ) score or score on spontaneous speech from WAB. In NN model for AQ score, 7 input valuables were selected by PIM; θ1 values of channel 2,3, and 11, θ2 values of channel 4, 9, and 13, and α value of channel 11. The average error of this model was 8.6 points, corresponding to the relative error of 10%. It was found that the model can estimate the AQ value at high accuracy. Another NN model to estimate the score on spontaneous speech was also constructed. The average error of this model with actual WAB score was 1.8 points. Predicted score of patient with motor aphasia coincided well with the actual score.