The CFT 20-R is often used to assess fluid intelligence. Hence, it can also be utilized to assess giftedness. The present study is concerned with an investigation of psychometric properties of the test with respect to measurement invariance between students of normal and higher intelligence. Analyses were conducted both at the item and scale level. A sample of N = 1886 male and female students from the lower, middle, and higher track of the German education system were administered the short form of the CFT 20-R. Comparing students of normal (IQ < 120) and higher (IQ ≥ 120) intelligence, DIF analyses at the item level revealed that measurement invariance was largely observed with respect to item difficulties but not discrimination parameters. Partial strong measurement invariance was observed at the subtest level. The CFT 20-R is therefore well-suited for a first screening of intellectual giftedness.