This study aimed to investigate gifted students' problem posing abilities requiring arithmetical operations with natural numbers. In the present study, the descriptive research model has been used which is one of the quantitative research methods. The research sample was composed of 25 fourth grade primary school students. All of the students were studying in science and arts center located in a province in the Eastern Anatolia region of Turkey. In the study, Problem Posing Form, consisting of six items for arithmetical operations with natural numbers was used as data collection tool. The problems posed were analyzed according to the semantic structures. According to the findings, it was determined that gifted students posed problems using different semantic structures that requiring arithmetical operations with natural numbers. However, it was determined that some semantic structures were used more frequently in problems. Accordingly to this, it has emerged as most frequently used semantic structures in problems, join for addition, separation for subtraction, repeated addition for multiply and sharing for division operations. Also, it was determined that some gifted students experienced problems such as using different arithmetical operation, writing the exercises, not responding, and making logical mistakes. In the light of findings, it has recommended that problem posing activities involving different semantic structures should be included in differentiated mathematics curriculum to be developed for gifted students. It is suggested to investigate gifted students' problem posing abilities in the context of creativity in later studies.