Objective To understand the neuropsychological development status and catch-up characteristics of late preterm infants (LPI), and to explore the longitudinal association between parent-child interaction and neuropsychological development. Methods A retrospective cohort study was conducted on 888 children who completed regular follow-ups at corrected ages of 12 to 36 months at the Department of Child Healthcare of Guiyang Maternal and Child Health Hospital between January 2022 and August 2025. Participants were divided into LPI group (n=215) and full-term group (n=673) based on gestational age. Neuropsychological development and parent-child interaction were assessed at corrected ages of 12, 24, and 36 months using the Gesell Developmental Schedule and the Parent-Child Interaction Scale. Linear mixed-effects models were employed to examine the longitudinal effects of parent-child interaction on neuropsychological development. Results At corrected age 12 months, the LPI group showed the highest rate of developmental delay in the language domain (12.6%, 27/215), followed by gross motor delay (8.8%, 19/215). At corrected ages 12 and 24 months, the DQ scores of all developmental domains in the LPI group were significantly lower than those in the full-term group (P<0.05). By corrected age 36 months, except for language, no significant differences were found between groups in other domains (P>0.05). At corrected age 12 months, parent-child interaction was positively correlated with language DQ in the LPI group (B=0.172) and personal-social DQ in the full-term group (B=0.097) (P<0.05). At corrected age 24 months, parent-child interaction was positively correlated with all DQ domains in the LPI group (B_{adaptive behavior}=0.282, B_{gross motor}=0.309, B_{fine motor}=0.227, B_language=0.448, B_{personal-social}=0.271, B_{total DQ}=0.302). In the full-term group, correlations were found in gross motor (B=0.117), language (B=0.253), and total DQ (B=0.118) domains (P<0.05). At corrected age 36 months, parent-child interaction was positively correlated only with language DQ in the full-term group (B=0.216). Linear mixed-effects models showed significant positive predictive effects of parent-child interaction on language (β=0.09), personal-social (β=0.08), and total DQ (β=0.04) in both groups (P<0.05). Significant interaction effects of group × parent-child interaction were observed for gross motor (β=0.10), language (β=0.14), and total DQ (β=0.09) (P<0.05). Conclusions Neuropsychological development in late preterm infants lags behind that of full-term infants. Positive parent-child interaction effectively promotes neuropsychological development in late preterm infants.