In order to better understand the behavior of the human brain, it is very important to perform large scale neural network simulation which may reveal the relationship between the whole network activity and the biophysical dynamics of individual neurons. However, considering the complexity of the network and the large amount of variables, researchers choose to either simulate smaller neural networks or use simple spiking neuron models. Recently, supercomputing platforms have been employed to greatly speedup the simulation of large brain models. However, there are still limitations of these works such as the simplicity of the modeled network structures and lack of biophysical details in the neuron models. In this work, we propose a parallel simulator using biophysically realistic neural models for the simulation of large scale neural networks. In order to improve the performance of the simulator, we adopt several techniques such as merging linear synaptic receptors mathematically and using two level time steps, which significantly accelerate the simulation. In addition, we exploit the efficiency of parallel simulation through three parallel implementation strategies: MPI parallelization, MPI parallelization with dynamic load balancing schemes and Hybrid MPI/OpenMP parallelization. Through experimental studies, we illustrate the limitation of MPI implementation due to the imbalanced workload among processors. It is shown that the two developed MPI load balancing schemes are not able to improve the simulation efficiency on the targeted parallel platform. Using 32 processors, the proposed hybrid approach, on the other hand, is more efficient than the MPI implementation and is about 31X faster than a serial implementation of the simulator for a network consisting of more than 100,000 neurons. Finally, it is shown that for large neural networks, the presented approach is able to simulate the transition from the 3Hz delta oscillation to epileptic behaviors due to the alterations of underlying cellular mechanisms.