This study examines the impact of L1 reading ability on L2 reading under different cognitively demanding tasks taking 206 non-English majors as sample with SEM. The results show that the contribution of L1 reading ability to L2 reading differs under the different cognitively demanding tasks. Besides, with the improvement of L2 proficiency of readers, the influence of L1 reading ability on L2 reading shows the change from insignificance to significance under high cognitively demanding tasks, and shows increasing intensity under low cognitively demanding tasks. At last, in the second language reading teaching, teachers should carry out adaptive instruction for students with different levels of second language under different cognitively demanding tasks.