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This paper proposed a three-dimensional (3D) surface denoised tracking algorithm based on adaptive 3D fractional-order integral to reconstruct high accuracy edge surfaces from the noisy medical CT slices. The fractional-order integral could weaken high frequency signal and strengthen low frequency signal at the same time. The proposed algorithm just used the fractional-order integral to weaken noise and keep images' original detail information as much as it could. This paper proposed the adaptive 3D fractional-order integral based on gradient information. It added the adaptive 3D fractional-order integral algorithm to the 3D edge surface tracking algorithm to overcome the shortcoming caused by the Laplacian operator in traditional edge surface tracking algorithm. Experiments show that the adaptive 3D fractional-order integral can effectively track edge surfaces from noisy medical CT slices with high accuracy. The denoised results are better than specified fractional-order integral. [ABSTRACT FROM AUTHOR]