The electric potential of linear charge in an infinite rectangular cavity filled with anisotropic dielectric is the boundary value problem of Poisson equation in anisotropic media. The electric potential of linear charge in the infinite rectangular cavity is solved by using method of eigenfunction and method of separation of variables,when the walls of the cavity meet the first homogeneous boundary conditions or meet the first nonhomogeneous boundary conditions. The results can apply to isotropic dielectric in the situation: ε11=ε22=ε33=ε.