Mathematically gifted students have a potential for understanding and connecting mathematics concept. Pattern generalization as a part of functional thinking becomes one of the benchmarks for gifted students in mathematics. The mathematics curriculum in Indonesia that has not accommodated the functional thinking ability of elementary school students is the basis for this study. It focuses on describing mathematically gifted students functional thinking in solving figural and non-figural linear pattern task. Functional thinking abilities in this study consist of thinking process in near generalization, far generalization, formal generalization and determine inverse. Case study of qualitative approach used in describing mathematically gifted students thinking. Data were collected from 5th-grade of gifted student's problem solving in figural and non-figural linear patterns task. The finding showed that gifted students are able in functional thinking in different ways. They represented the relationship of two quantities symbolically. In solving figural linear pattern task, gifted students perform FT consist of: near generalization by counting, multiplicative approach, and contextual strategy; far generalization by contextual strategy; formal generalization by multiple difference and proportional strategy; and determine inverse by using general rule. In solving non-figural linear pattern task, gifted students perform FT consist of near generalization, far generalization, and formal generalization by multiple difference strategy; and determine inverse by using general rule.