The feasibility to measure the inner diameter and wall thickness of a micro-capillary by using digital holographic tomography was explored. As the micro-capillary had an ideal cylindrically symmetric structure, the single reconstructed data under zero incidence angle were used to simulate all measured field data under different angles. A tomography was performed for the micro-capillary by a filtered back-projection algorithm and a Fourier diffraction algorithm respectively to reconstruct the 3-D map of refractive index. According to the 3-D distribution of refractive index, the size of inner diameter and wall thickness of micro-capillary were obtained by the related edge detection algorithm of image processing. Experimental results show that diffraction tomography based on the Rytov approximation can better response the dimensions of the micro-capillary than the filtered back-projection reconstruction algorithm for tiny weakly-diffracting objects under the condition of reasonable light path environment of the hologram recording. It proves that the digital holographic tomography can measure the inner diameter and wall thickness of the micro-capillary exactly and can provide a new way for the nondestructive measurement of tiny weakly-diffracting objects.