This study investigates the human intellectual cognitive process, individual’s different strategies and process time variations while performing a simple mathematical task. An adaptive control of thought-rational (ACT-R) cognitive architecture is adopted to model the cognitive process. Two participants were recruited for this study and performed a mental summation task on a developed experiment software. The participant’s eye gaze movement and answering time were recorded and analyzed. The cognitive process parameters of the model have been determined in the model in order to simulate their cognitive process. The results show a different cognitive process between the first and the second participants which indicates that each participant has his/her own cognitive process characteristics to perform. The model not only demonstrates the detailed mechanism of human intellectual concentration but also reproduce process time variations in the cognitive process.