Recently computer graphics and CAD systems of many kinds have been developed. and this trends will be more increased in the future because the application fields are diverse However, data exchange problems between these systems will be occurred as the system kinds increase. Standards for solving these problems are made by IGES and STEP. etc, Nevertheless, it is unsatisfactory now because data exchange between different systems is not running well with reliability and efficiency. Because vendors implement with different ways, data exchange of the curves and surfaces between different systems which are based in the geometric modeling system, does not satisfy. This paper is a research for curve conversion in the data exchange between different systems. Also this paper analyzed the transferring data which are effectively conversed the curves among the four different types of curves in the less important curve shape environment.