In this article, we use cusp catastrophe model for analyze the intelligence. Definition of intelligence is restricted by IQ that can be separated to two aspects, those are Concrete-Practice (CP) and Theoretical-Verbal (TV). We will demonstrate that two students of university with the same aspect of intelligence, CP, but have different TV will state in different department of a university. We must get the critical point that differentiate the characteristic of one department with the others. Moving from one department to the other caused by the change of TV will occur as a jump. This jump will determined cusp catastrophe model. Catastrophe theory provides a universal method for the study of all jump transitions, discontinuities, and sudden qualitative changes. Especially in mathematical understanding, catastrophe theory is a part of singularities theory and bifurcation theory. The samples were the psychological testing, IST, results of 428 ITB's students. The first step is Confirmatory Factor Analysis application to reduce nine psychotest variables to get two control variables that construct cusp catastrophe model. The second step is fitting the model of cusp catastrophe to the data with Cuspfit procedure. As measurement of goodness of fit, Cuspfit procedure uses the Akaike Information Criterion (AIC) and Bayes Information Criterion (BIC). The model with the lowest AIC and BIC is selected.