The human brain is highly plastic. Cognitive training can make a change in functional connections between brain regions. The structures of brain networks may determine its dynamic behavior which is related to human cognitive abilities. To study the effect of functional connectivity on the brain dynamics, a dynamic model is established based on functional connectivity of the brain and the Hindmarsh-Rose model in this work. The resting-state fMRI data from the experimental group undergoing abacus-based mental calculation (AMC) training and from the control group are used to construct the functional brain networks. The local efficiency and global efficiency of the functional brain networks of the experimental group are higher than those of the control group. The dynamic behavior of brain at the resting and task states for the AMC group and the control group are simulated based on above dynamic model. In the resting state, some different activated brain regions exist between the AMC group and the control group. A stimulus with sinusoidal signals to brain networks is introduced to simulate the brain dynamics in the task states. The dynamic characteristics are extracted by the excitation rates, the response intensities and the state distributions. The change in the functional connections of brain regions with the AMC training would in turn improve the brain response to external stimulus, and make the brain more efficient in processing related tasks.