Abstract: In spatial hearing, a complex valued head--related transfer function (HRTF) can be represented as a real valued head--related impulse response (HRIR). Using Karhunen-Loeve expansion, the spatial features of the normalized HRIRs on measurement space can be extracted as spatial characteristic functions. A neural network model based on Von-Mises function is used to approximate the discrete spatial characteristic function of HRIR. As a result, a time domain binaural model is established which well fits the measured HRIRs.