Based on the two spin orbit coupling parameter model and the complete energy matrices for a d3 configuration ion in a trigonal ligand field, the local structure and the ground-state splitting of Cr3+ ion in Cs2NaMF6(M=Al, Ga):Cr3+ systems have been studied. By simulating the EPR parameter D and the optical spectra, the distorted angles of two inequivalent sites formed by Cr3+ replacing M3+ are determined and the obvious difference of the distorted angles Δθ calculated by using two spin orbit coupling parameter model and single spin orbit coupling parameter model is found. Our results indicate that the influence of ligand F- can not be ignored with respect to spin orbit coupling mechanism when the energy level fine structure and local structure distortion of fluoride complex molecules are studied. Meanwhile, the dependence of EPR parameter D on angle θ, average parameter ζ1 and divergent parameter ζ2 is discussed, respectively.