This study systematically examines the moderating effects of task type and L2 proficiency on the relationship between L1 and L2 simultaneously across reading and writing tasks with different levels of cognitive complexity. Main and moderating effects were evaluated through structural equation modeling analyses. First, both L1 skills and L2 proficiency were significant independent predictors of L2 reading and writing performance across tasks with different levels of cognitive complexity. Second, L2 proficiency had a much greater effect on L2 reading and writing performance across tasks with different cognitive loads than L1 skills. Third, the strength of the relationship between less cognitively demanding L1 and L2 reading tasks showed no significant difference between the low- and high-L2-proficiency groups. Fourth, the strength of the relationship between more cognitively demanding L1 and L2 reading tasks showed a significant difference between the low- and high-L2-proficiency groups. Fifth, the strength of the relationship between L1 and L2 writing tasks with different levels of cognitive complexity varied significantly depending on the level of L2 proficiency. These results are discussed theoretically and pedagogically.