Stable homotopy category is an important object in studying algebraic topology, and in the last thirty years, people have been trying to use chromatic homotopy theory and algebraic geometry to study its filtration structure. Specifically, stable homotopy category has a natural symmetric tensor product structure and tensor unit, which make it resembles a commutative ring with unit, so we could introduce the method of algebraic geometry and define “prime ideal” and “spectrum” for it. Besides, the Zariski topology of the “spectrum” characterizes the filtration structure of stable homotopy category. Therefore, the computation of this “spectrum” (called Balmer spectrum) is of great significance. The computation of Balmer spectrum of stable homotopy category has been completed in the end of last century, naturally, people want to compute the Balmer spectrum of G-equivariant stable homotopy category. In fact, the computation of Balmer spectrum consists two parts: set structure and Zariski topology structure. In 2017, the work of Balmer and Sanders published in Invent.Math. determined the set structure of Balmer spectrum when G is a finite group and the topology structure of Balmer spectrum when G is a cyclic group Z/p of prime order p; In 2019, the work of Barthel, Hausmann, Naumann, Nikolaus, Noel and Stapleton also published in Invent.Math. obtained the topology structure of Balmer spectrum when G is a finite abelian group. While the computation of Balmer spectrum is of great concern for many people, this work is still not finished. Hence, this dissertation provides a new method that can cover the work of our predecessors whom compute Balmer spectrum when G is a finite abelian group. Meanwhile, this new method offers an explanation for the blue-shift phenomenon.    When G is a finite abelian group, the set structure of Balmer spectrum is determined by Balmer and Sanders, and its element is the “prime ideal” P G (H,p,m) characterized by three parameters: the subgroup H of G, prime number p, and chromatic height m. Hence the remaining work is to compute the topology structure of Balmer spectrum. And it is necessary for the computation of the topology structure to determine whether any two “prime ideals” P_G (K,q,l), P_G (H,p,m) have the relation of inclusion. The present knowledge shows that the necessary condition of P_G (K,q,l) ?  P_G (H,p,m) is p = q,K