A scalefree neural network was constructed based on a twodimensional mapbased model. and Gaussian white noise was used to imitate the noisy environments of biological neural systems. The effect of noise on the dynamics of the network was studied by numerical simulation. It is found that adding the noise can enhanc the neurons excitability, even induce spikes. When the noise intensity is appropriate, the regularity of spike series achieves the best, where coherence resonance happens. Moreover, simulation results indicate that the change of structure and parameters of the neural network has an important effect on the resonance characteristics.