Socioeconomic status (SES) is associated with childhood anthropometry, but little is known about how it is associated with tissue growth and body composition. To investigate this, we looked at components of SES at birth with growth in early and mid-childhood, and body composition in a longitudinal study in Nepal. The exposure variables (material assets, land ownership, and maternal education) were quantified from questionnaire data before birth. Anthropometry data at birth, 2.5 and 8.5 years, were normalized using WHO reference ranges and conditional growth calculated. Associations with child growth and body composition were explored using multiple regression analysis. Complete anthropometry data were available for 793 children. There was a positive association between SES and height-for-age and weight-for-age, and a reduction in odds of stunting and underweight for each increase in rank of SES variable. Associations tended to be significant when moving from the lower to the upper asset score, from none to secondary education, and no land to >30 dhur (~500 m2). The strongest associations were for maternal secondary education, showing an increase of 0.6–0.7 z scores in height-for-age and weight-for-age at 2.5 and 8.5 years and 0.3 kg/m2 in fat and lean mass compared to no education. There was a positive association with conditional growth in the highest asset score group and secondary maternal education, and generally no association with land ownership. Our results show that SES at birth is important for the growth of children, with a greater association with fat mass. The greatest influence was maternal secondary education.