In coherent optical-fiber communication systems, polarization-division multiplexing is employed to double the transmißion capacity. Polarization tracking based on digital signal proceßing (DSP) is used to cope with the polarization fluctuations of the light wave, which are caused by disturbances of the optical fibers. Usually, the polarization demultiplexing and polarization tracking are performed by using butterfly-structured finite impulse response (FIR) filters. We have proposed and investigated novel methods of polarization tracking using artificial neural networks (ANNs). An ANN can perform polarization demultiplexing because an ANN includes butterfly structures. Adaptive control of the weights of the ANN can be achieved by using decision directed least mean squares (DD-LMS) algorithm. Furthermore, the ANNs can potentially compensate waveform distortion caused by optical nonlinear effects such as self phase modulation (SPM) and croß-phase modulation (XPM). In this paper, we investigated the polarization tracking performance of the ANN under various conditions of polarization fluctuation speed by numerical simulations, comparing with that of FIR filters. Furthermore, we investigated the tracking performance depending on the number of input layer and hidden layer units of the ANN. The results show that the ANN can efficiently track the polarization fluctuation.