A novel discrimination method of Parkinsonian tremor from essential tremor is presented in this paper. The method uses the approximate power spectral density of specific sub-bands, which is estimated using a soft-decision wavelet-based decomposition of EMG and accelerometer signals. Selection of specific sub-bands of the spectrum of two EMG signals and accelerometer signal has been implemented to provide the neural network with its proper inputs. Two sets of data, training set and test set, which are recorded in the department of Neurology of the University of Kiel-Germany, are used in this work. The training set, which consists of 21 essential tremor subjects and 19 Parkinson disease subjects, is used to train the neural network of type feed-forward back-propagation. The test set, which consists of 20 essential tremor subjects and 20 Parkinson disease subjects are used to test the performance of the discrimination system. A best discrimination efficiency of 87.5% has been obtained in this work.