A numerical study of a perturbed sine-Gordon equation (SGE) in an annularly symmetric Josephson junction by considering the cosΦ-term is carried out in this paper. The numerical results show that in the absence of external applied field there are two branches of the zero field steps (ZFS) in the I-V characteristic; the lower voltage ZFS corresponds to the single soliton excitation (1-ZFS) and the higher voltage one corresponds to three solitons exicitation (3-ZFS). In our calculations for the definite size and parameters of the annularly symmetric Josephson junction, the two solitons excitation is unstable. The three solitons excitation is similar to the 3-ZFS with the symmetric mode in the one-dimensional overlap Josephson junction except that there exist amplitude molulation for the time behaviour in both of the voltages 〈φτ〉ρ and φτ(ρ1,τ).