Based on the two-dimensional neural map, we use the Gaussian white noise to imitate the noisy environments of neurons. We investigate the impacts of Gaussian white noise on the phase diagram of parameters. It is found that adding the noise leads to an enhancement of excitability of the system. We also study the coherence resonance (CR) by numerical simulation, and the parameter condition of the CR phenomenon is discussed. Only when the parameters of the system are chosen in the regime of silence and near the dividing line between spiking and silence can we get the CR phenomenon.