Abstract: A least squares method for identification of non-integer order systems is introduced into frequency domain and an algorithm is presented. The verification was performed on systems with known parameters. Results show that non-integer order systems have important advantages over integer order systems: We can achieve better fittings of the frequency response data with simpler models for non-integer order systems; We can achieve the best integer-order model that fit the measured frequency response data by scanning orders for integer-orders systems; The algorithm is numerically more stable than in the case of integer order.