As the biological neural networks have small-world property and updating connection weights with time, we accordingly propose a new model of small-world biological neural networks based on biophysical Hodgkin-Huxley(H-H)neurons with updated weights. Then we study the statistical properties of excitement of this model and the updating of weights. The results show that, for networks with the same structure and parameters and external stimulation, there exists an optimal learning rate ralue b* which makes the excitement strength of biological neural networks strongest.