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The nature of individual differences among children is an important issue in the study of human intelligence. There are close relation between intelligence and executive functions. Traditional theories, which are based mainly on the factor analysis, approach the problem only from the perspective of psychometrics. However, they do not study the relation of cognition and neurobiology. Some researchers try to explore the essential differences in intelligence from the basic cognitive level, by studying the relationship between executive function and intelligence. The aim of this study was to do the followings 1) to delineate and separate the executive function in children into measurable constructs; 2) to establish the relationship between executive function and intelligence in children; 3) to find out the difference and its neural mechanism between intellectually-gifted and normal children’s executive function. The participants were 188 children aged 7-12 year old. There were 6 executive function tasks. The results were follows: 1) The latent variables analyses showed that there was no stable construct of executive function in 7-10 year old children. The executive function construct of 11-12 year old children could be separated into updating, inhibition and shifting. And they had grown to be more or less the same as adults in the executive function. There were only moderate correlations between the three types of executive function, but they were largely independent of each other. 2) The correlations between the indices of updating, inhibition, shifting and intelligence were different in 7-12 year old children. The older the age, the more the indices were related to intelligence. The updating and shifting were related to intelligence in 7-10 year old children. There were significant correlations between the updating, inhibition, shifting and intelligence in 11-12 year old children. The correlation between updating and intelligence was higher than the correlation between shifting and intelligence. Furthermore, in structural equation models controlling for the three executive functions correlations, updating was highly related to intelligence, but the relations of inhibition and shifting to intelligence were not significant. 3) Intellectually-gifted children performed better than normal children in executive function tasks. The neural mechanism differences between intellectually gifted and average children were indicated by ERP component P3. The present study helps us to understand the relationship between intelligence and executive function; and throws light on the issue of individual differences in intelligence. The present results can provide theoretical support for the development a culture-free intelligence test and a method to promote the development of intelligence. Our present study lends support to the neural efficient hypothesis.