Small-angle x-ray scatter imaging has a high intrinsic contrast in cancer research and other applications, and provides information on molecular composition and micro-structure of the tissue. In general, the implementations of small-angle coherent scatter imaging can be divided into two main categories: direct tomography and angular dispersive computerized tomography. Based on the recent development of energy-discriminative photon-counting detector array, here we propose a computerized tomography setup based on energy-dispersive measurement with a photon-counting detector array. To show merits of the energy-dispersive approach, we have performed numerical tests with a phantom containing various tissue types, in comparison with the existing imaging approaches. The results show that with an energy resolution of ~6 keV, the energy dispersive tomography system with a broadband tabletop x-ray would outperform the angular dispersive system, which makes the x-ray small-angle scatter tomography promising for high-specificity tissue imaging.