Abstract: The plasma tensor dielectric permittivity and electromagnetic wave accurate expressions in the arbitrary axial magnetic field are obtained from the Maxwell’s equations and the double component plasma particle linear movement equations. It is showed that E wave and H wave can’t be separated in this kind of plasma wave-guide. The axial-symmetrical solutions for the field components are obtained, which have the same form as that in ref.［4］ with the single-wave-approximation. The electromagnetic wave accurate expressions are very important for the research of the interaction between the plasma and the electromagnetic wave.