Drug addiction is one of the chronic mental disorders that results in a compulsive behavior to seek and consume drug. Recent statistics show that about 15 of world population is addicted with some sort of drug. It has been reported that drug addiction causes structural such as change in volume of gray and/or white matter, and functional neuroplasticity such as changes in the concentration of neurotransmitter (dopamine, glutamate, GABA etc.). Functional neuroplasticity can either block or excite neurotransmission among the neurons, hence altering the functionality of neurons and disrupt the control mechanism in the reward pathway and finally leading to an uncontrolled behavior. In drug addiction, the occurrence of uncontrolled behaviors in the different regions of reward pathways can be modeled using brain circuit to map directly the neural activities. This paper discusses the biological & chemical processes and control mechanisms involved in drug addiction develops a model of brain circuit under the influence of drug. It is observed that reduced inhibitory neurotransmission of GABA and increased excitatory neurotransmission of Glutamate in different regions of brain circuit contributes to reorganization of control mechanism by impaired encoding in control regions (PFC and Cigulate Gyrus). As a result, the drug related reward is considered as reinforcement of drug taking. Furthermore, it is also argued that estimation and quantification of GABA and Glutamate may provide significant differences between normal and drug addict brain that will lead to development of drug addiction severity monitoring system. © 2014 IEEE.