This study compared EEG(Electroencephalogram) between elementary school students having a tendency to computer game addiction(CGA) and elementary school students scarcely using computer game(SCG). For this, 42 students(21 CGA, 21 SCG) from 5th grade of an elementary school in Seoul were selected. EEG was measured during performing left brain hemisphere typed cognitive tasks and the data of EEG by using linear and spectrum methods were statistically analysed. Brain function score by EEG(BQ Test) in 2 positions of brain(Fp1, Fp2) was calculated. It was revealed that brain activity level of CGA was lower than that of SCG and brain stress level of CGA was higher than that of SCG in performing cognitive tasks.