This study aimed to identify the psychological needs of high achievers -achieving students- in grade eleven of post-basic education in the Eastern region (North) of the Sultanate of Oman, and specifically has tried to answer the following research questions: 1- What are the psychological needs of high achieving students in grade eleven? And how can we order them according to their priority? 2- Are there significant statistical differences between the psychological needs of the high achieving students attributed to the following variables: gender, level of mother's and father's education, social status of parents and family's income? The researcher has a comprehensive survey of high achievers in grade eleven in all schools of basic education who got 90% or above at the end of the academic year 2008/2009. The total number of these students was (120). In order to answer the research questions of this study, the mean and standard deviations were calculated. The researcher used (t.Test) and analysis of varience (One Way-ANOVA). The results showed that the first psychological need of the talented is the need for tolerant and flexible teachers who understand their special needs. The second one is the need to increase the academic achievement, and the third is the need for assistance in investing their talents and energies in a productive way. Regarding the importance of high achievers' needs, they are listed in order of importance: occupational needs, cognitive needs, psychological needs and social needs. The results also showed no statistically significant differences at (0.05) in the psychological needs of talented students due to the changes of the following: gender, mother's educational level, social status of the parents. In contrast, there were statistically significant differences at (0.05) in the cognitive needs based on the educational level of the father. In addition, there were statistically significant differences at (0.05) in the occupational needs and social needs and the overall grade in the measure of psychological needs based on the variable of the family income. In order to realize the direction of those variable differences, Scheffe test was conducted, but the results did not show any statistically significant differences.