In this work, recognition of vowels in Turkish Language by probabilistic neural networks is implemented using a spectral analysis method. Power spectral density of the phones obtained from speakers is estimated. Then weighted power spectrum is calculated after power spectral density of that phone is passed through a number of band pass filters. In this way, estimated power spectrums of the phones which are obtained from speakers approximate to a mel scale. Mel scale coefficients obtained, form the feature vector of the phone that is pronounced. These feature vectors constitute the database of the related speaker. Thus and so, every speaker has its own database. When it comes to recognize a phone pronounced by a speaker later, a probabilistic neural network model is created using the database belonging to that speaker. The feature vector of the phone which is to be recognized is computed as mentioned above. In this study, speaker-dependent recognition of Turkish vowels has been realized with an accuracy rate of over 95 percent.