The development of the Cognitive Resource Theory by F.E. Fiedler was in large part due to Fiedler's expecting to be able to cope with those critics who clained that his Contingency Leadership Theory was a "black box". The main purpose of this theory was to clarify have those interactions among personality attribute, which were reflected by the LPC score, and situational factors affected leadership effectiveness. The subjects of this study included 163 principals and 872 teachers taken from a random sample of 163 elementary schools in the area of Taiwan. The major findings of this study were concluded as follows: l.In regard to the correlation between principals' cognitive abilities and their leadership performance, those principals who were under lower stress revealed higher correlation than those principals who were under higher stress. 2.The principal's experience did not predict performance. 3.The correlation between principal's cognitive abilities and performance were higher when they were highly directive behavior and teachers were highly supportive than they were highly directive behavior but teachers were not supportive. 4.Under conditions that principals were low directive behavior, the correlation between teacher cognitive abilities their performance were higher when teachers' group was highly supportive than the group was low supportive. 5.The degree of complexity of task contributed to the degree of correlation between principals' cognitive abilities and their performance.