In this paper, the effects of transverse mean velocity and temperature gradients on the acoustic propagation in a straight annular duct are studied so as to be the basis of further analyzing the sound propagation in nonuniform annular ducts. The wave equation governing this acoustic field is a difficult eigenvalue problem. The eigenvalue is solved by an IMSL package which is proposed to find suitable initial guess. By using the initial guess, in addition to the iterative process, the final results have been found. The results are proved to be of good accuracy by comparing with published data, and the errors are under 2.0%. From this paper we also find that, under the influence of the unsymmetric boundary condition, the attenuations of the axial symmetric radial mode are different from other modes, and this property of the former mode can not be expected by ray acoustic arguments, on the other hand, the attenuations of the lowest mode and the spinning modes can be expected.