The number of Chinese children living in poverty has risen steadily in Hong Kong, China. However, little is known on the longitudinal effects of family socioeconomic status (SES) on cognitive-linguistic skills, word reading and writing in children from low-SES backgrounds. This study examines differences in cognitive-linguistic skills and word reading and writing across kindergarteners from the low- and middle-SES groups. It also investigates the direct link between SES and children's concurrent Chinese literacy skills and how cognitive-linguistic skills mediate the longitudinal associations between SES and word reading and writing. One hundred and nine children were assessed at Kindergarten K2 (Time 1) and reassessed at Kindergarten K3 (Time 2). Children were administered the measures of vocabulary knowledge, phonological awareness, morphological awareness, executive functioning, Chinese word reading, and Chinese word dictation at both time points. Results revealed that low-SES children performed less well on Chinese word reading and dictation than their middle-SES peers at both time points. Moreover, hierarchical regression and mediation analyses suggested that SES had a direct relation with Chinese word reading at Time 1 after controlling for age and cognitive-linguistic skills, and an indirect link with Chinese word dictation at Time 2 which was fully mediated by phonological awareness and vocabulary knowledge at Time 1. The results highlight that SES may exert an impact on children's early Chinese reading and writing and suggest the benefit of improving phonological awareness and vocabulary knowledge of low-SES children.