Laser cooling of solid material is also called anti-Stokes fluorescent cooling, and it is a developing all-optical cooling technology in recent years. The key question of this cooling technique is to choose suitable materials. Taking Tm3+ ion as an example, relationship between the minimum energy gap and the laser pumping rate is analyzed, and the relationship between the energy gap and the cooling power as well as the relationship between the energy gap and the heat-light converting efficiency under the different pumping rate is studied, then the relationship between the optimal heat-light converting efficiency and the pumping rate is obtained. It is found that energy gap required in the cooling cycle should be at least 4500 cm-1. It is more appropriate to choose the energy gap at 5000～6000 cm-1. Finally, the feasibility of laser cooling of thulium-doped material and the choice of host material are briefly discussed.