A decrease in alpha band power is defined as a hallmark of electroencephalogram (EEG) in Alzheimer's disease (AD). This study devotes to understanding the neuronal correlates of alpha rhythm slowing associated with AD from the view of neurocomputation. Firstly, a modified computational model of thalamo-cortico-thalamic (TCT) circuitry is constructed by incorporating two important biologically plausible ingredients. One is the disinhibition property between different inhibitory interneurons in the cortical module. The other is the full relay function of thalamic relay nucleus (TCR) to the cortical module. Then, by decreasing synaptic connectivity parameters to mimic the neuropathological condition of synapse loss in AD, the correlation between neuronal synaptic behavior and abnormal alpha rhythm is simulated by means of power spectral analysis. The results indicate that these decreases of synaptic activity, i.e., not only the excitatory synaptic connections from TCR to fast inhibitory interneurons Cfte and from excitatory interneurons to pyramidal neurons Cpxe but also the inhibitory synaptic connections from fast inhibitory interneurons to slow inhibitory interneurons Clfi and from inhibitory interneurons to TCR Ctii, can significantly diminish the peak power density over the alpha band of the thalamic output, which implies that there is a slowing of alpha band. Furthermore, the underlying mechanism behind the alpha rhythmic changes is analyzed using nonlinear dynamical technique. The results reveal that decreases of Cfte, Cpxe, Clfi and Ctii can make the thalamic module transfer from a limit cycle mode to a point attractor mode, which may lead to the alpha rhythm slowing in the modified TCT model. We expect this work can be helpful in identifying early biomarkers of AD's EEG and understanding potential pathogenesis of AD.