The aim of this study was to analyze the influence of economic capital, culture capital, social capital, social security, and living conditions on children's cognitive ability. However, most studies only focus on the impact of family socio-economic status/culture capital on children's cognitive ability by ordinary least squares regression analysis. To this end, we used the data from the China Family Panel Studies in 2018 and applied proxy variable, instrumental variables, and two-stage least squares regression analysis with a total of 2647 samples with ages from 6 to 16. The results showed that family education, education expectation, books, education participation, social communication, and tap water had a positive impact on both the Chinese and math cognitive ability of children, while children's age, gender, and family size had a negative impact on cognitive ability, and the impact of genes was attenuated by family capital. In addition, these results are robust, and the heterogeneity was found for gender and urban location. Specifically, in terms of gender, the culture, social capital, and social security are more sensitive to the cognitive ability of girls, while living conditions are more sensitive to the cognitive ability of boys. In urban locations, the culture and social capital are more sensitive to rural children's cognitive ability, while the social security and living conditions are more sensitive to urban children's cognitive ability. These findings provide theoretical support to further narrow the cognitive differences between children from many aspects, which allows social security and living conditions to be valued.