Taking the encircled-power width defined by the power of 86.5% in the bucket as the characteristic parameter, the spreading of annular beams propagating through atmospheric turbulence along a slanted path is studied by using the numerical simulation method. It is shown that in free space, the lobe of the far-field intensity distribution appears with the obscure ratio increasing. The lobe disappears due to the turbulence, and the far-field intensity distribution is not a Gaussian profile. The beam spreading increases as the obscure ratio and the zenith angle increase, and the influence of turbulence on the beam spreading increases when the zenith angle increases. However, when the obscure ratio is large or small, the influence of turbulence on the beam spreading decreases as the obscure ratio increases; when the obscure ratio is middling, the influence of turbulence on the beam spreading is nearly unchanged versus the obscure ratio. Compared with previous work, it is found that the law of the influence of turbulence on the spreading of annular beams is different if the percentage of the power in the bucket is different. The results are useful for practical applications.