Laser medium for solar-pumped solid laser of 10MW-1GW power is a key to realize Laser Space Solar Power System (L-SSPS). Since it is an ultrahigh power system operated in space, the laser medium must satisfy the conditions such as high efficiency, high power per weight or volume, excellent durability and maintainability, thermal equilibrium operation, and excellent long-range propagation of oscillated laser. YAG (Y3Al5O12) ceramics doped doubly with Nd and Cr is considered to be a suitable laser medium for L-SSPS at present. There are the following important points for L-SSPS application: 1) Optimization of the doping amount, 2) Process, 3) Temperature control. Feasibility of YAG ceramics is discussed from a view point of material science and proposed a YAG ceramics structure with graded distribution of dopants.