Effect of the nonlinear spatial modulation on the evolution of twocomponent linear coupling Bose-Einstein condensate bright solitons trapped in a harmonic potential has been investigated numerically.It is indicated that the atomic density envelope of the soltions is changed with the spatial variation of s-wave scattering length,and the soliton exists in stable state under appropriate conditions.The evolution of solitons depends on the sign and value of the coefficient of the nonlinear spatial modulation.