Compton scatter tomography can reconstruct the electron density distribution using the first-order Compton scattered photons, and has the potential of identifying different materials. However, in Compton scatter tomography, the detected photons may come from all voxels illuminated by the x-ray beam and the information is blended. Although the mixing could be reduced using mechanical collimation, the detected photon number will decrease seriously, which tampers the reconstructed image quality greatly. This paper proposes a Compton scatter tomography scheme based on the scatter physics and photon-counting detector. The Compton scatter photons could be detected without mechanical collimation while fan-beam CT scanning, and scattered signal can be separated into signals emitted from subsets of the entire volume due to geometry constraints associated with energy selection of the photon-counting detector. An analytical model of first-order Compton scatter projection procedure is constructed, and a compressed sensing based method is utilized to reconstruct the electron density distribution. Experiment results demonstrate the accuracy of the signal acquisition model, and the proposed imaging scheme can represent the anatomical structure of the object in electron density.