This paper introduces the intersection of polynomial ideals with parametric coefficients using Gröbner systems. Building on the existing understanding of polynomial ideals with numeric coefficients, we propose an intersection system and its computational algorithm that divides the parameter space into a finite set of cells, allowing us to calculate the intersection of the ideals within each cell. This approach enhances comprehension of polynomials and equips researchers and engineers with tools to gain deeper insights into mathematical models involving parametric coefficients. Consequently, it supports thorough examinations essential for tackling complex challenges in science and engineering. The functionality of the proposed algorithm has been implemented in the Maple software environment, which is well-suited for symbolic computation. The paper presents two examples: the first illustrates the intersection of two parametric polynomial ideals, and the second addresses a more complex scenario involving three such ideals. These examples showcase the practical application and effectiveness of the algorithms, highlighting their significance in the field. Finally, the CIS algorithm's performance is demonstrated through comprehensive intersection system computations on several examples.