Structure of semantic memory was investigated in the way of neural network simulations in detail. In the literature, it is well-known that brain damaged patients often showed category specific disorder in various cognitive neuropsychological tasks like picture naming, categorisation, identification tasks and so on. In order to describe semantic memory disorder of brain damaged patients, the attractor neural network model originally proposed Hinton and Shallice (1991) was employed and was tried to re-evaluate the model performance. Especially, in order to answer the question about organization of semantic memory, how our semantic memories are organized, computer simulations were conducted. After the model learned data set (Tyler, Moss, Durrant-Peatfield, & Levy, 2000), units in hidden and cleanup layers were removed and observed its performances. The results showed category specificity. This model could also explain the double dissociation phenomena. In spite of the simplicity of its architecture, the attractor neural network might be considered to mimic human behavior in the meaning of semantic memory organization and its disorder. Although this model could explain various phenomenon in cognitive neuropsychology, it might become obvious that this model had one limitation to explain human behavior. As far as investigation in this study, asymmetry in category specificity between animate and inanimate objects might not be explained on this model without any additional assumptions. Therefore, further studies must be required to improve our understanding for semantic memory organisation.