Non-Gaussian diffusion is commonly considered as a result of fluctuating diffusivity,which is correlated in time or in space or both.In this work,we investigate the non-Gaussian diffusion in static disordered media via a quenched trap model,where the diffusivity is spatially correlated.Several unique effects due to quenched disorder are reported.We analytically estimate the diffusion coefficient Ddis and its fluctuation over samples of finite size.We show a mechanism of population splitting in the non-Gaussian diffusion.It results in a sharp peak in the distribution of displacement P(x,t)around x = 0,that has frequently been observed in experiments.We examine the fidelity of the coarse-grained diffusion map,which is reconstructed from particle trajectories.Finally,we propose a procedure to estimate the correlation length in static disordered environments,where the information stored in the sample-to-sample fluctuation has been utilized.