Computed tomography (CT) allows the three-dimensional internal structure reconstruction of an object illuminated with X-ray light. In CT, a set of two-dimensional projections are taken to reconstruct the underlying object structure. The number of projections needed for sensing a CT scene is determined by the Nyquist limit. In some cases, the imposed projections number is excessive. Compressive sensing (CS) has emerged as a new sampling technique requiring fewer projections than those specified by the Nyquist criterion. Instead of measuring the simples directly, they are encoded before being integrated into the detector. This paper describes a CS system for CT based on coded apertures. An optimized value of transmittance and an aperture distribution are selected such that the quality of reconstruction is maximized. Simulations show that results in reconstruction with 50% of measurements are comparable with the traditional CT method based on Nyquist criterion. Similarly, results indicate that the PSNR of reconstructed images can be controlled according to the number of projections taken.