We study the effects of random long-range connections (shortcuts) on the firing patterns in a network composed of Hindmarsh-Rose neurons. It is found that the system can achieve the transition of neural firing patterns from the lower period state to the higher one, when the number of shortcuts in the neural network is greater than a threshold, indicating that the nervous system may make the optimal response to the change of stimulation by a corresponding adjustment of the shortcuts. Then we discuss the transition degree of firing patterns of neural network and its critical characteristics for different external stimulation current. Furthermore, the influences of coupling strength on such transition behavior of neural firing patterns are also considered. Our results may be useful in comprehending the real mechanism in neural coding and information transmission in neurobiological systems.