Based on Kummer model in nonlocal nonlinear medium, we study transmission characteristics of Kummer soliton. The results show that there is a group of two-dimensional Kummer-Gaussian soliton clusters, such as ring solitons, necklace solitons and lune solitons. Numerical simulation shows that Gaussian solitons and ring solitons are stable, while other solitons are not stable. Nonlinear modulation coefficient and modulation depth parameters have an important influence on the stability of the soliton, with their increase, the stability of the soliton improves.