Individuals with higher intelligence are not only defined as those who score high on an intelligence test, but also take into account other factors that influence individuals, such as social, environmental, and personality factors that together define a gifted person. Among these factors we can include anxiety and psychological well-being. Anxiety is the emotional reaction to the perception of danger or threat, originating through a set of responses linked to the cognitive system. Currently, anxiety affects many societies, therefore, it can influence and affect the psychological well-being of human beings. Is it possible to argue that there is a relationship between the level of intelligence of an individual with these emotional factors such as anxiety and psychological well-being? The objective of this research is to compare the following variables: Intelligence, Anxiety and Psychological Well-being in a sample of adolescents, with superior intelligence and average intelligence. The results of this research provide contributions to society and psychology.