In this paper, we present a model for the noise in narrow-band power line communication. We first derive a statistic model for the distribution of noise in a narrowband power line. The noise consists of three parts such as impulse noise, background noise, and narrow-band interference. For each part, we analyze its characteristics with the Markov Chain Monte Carlo (MCMC) method. The model is evaluated with extensive field measurement data and compared with a classical noise model. The evaluation results show that the proposed model can approximate the noise in narrow-band power line more accurately.