Prior research has mostly focused on either basic language or basic cognitive precursors of reading development, but relatively little is known about their relative importance for reading, especially for Chinese beginning readers. The present study examined whether and how basic cognitive processing (executive function, attention, and visual-spatial perception) and basic language processing (phonological awareness, morphological awareness, orthographic awareness, and RAN) measured at kindergarten influence Chinese character reading and reading comprehension in the first grade. Results showed that basic language abilities including morphological awareness and rapid automatized naming predicted later Chinese character reading. Only one basic cognitive skill, sustained attention, predicted later reading comprehension. Mediation analysis showed that the overall effects of basic cognitive skills on later character reading and reading comprehension were mediated by basic language skills. These findings supported an integration reading model for early Chinese reading and basic language processing at kindergarten plays an important role in explaining the relation between basic cognitive processing and grade one reading performance.