The rapid acquisition of projective images with low radiation dose is essential in computed tomography with diffraction enhanced imaging to extract absorption, refraction, and scattering images from weakly absorbing specimens. This plays a critical role in applying diffraction enhanced imaging to biological and medical imaging. In this study, an improved diffraction enhanced imaging method is proposed to rapidly implement X-ray trimodal computed tomography. This method positions the sample in a specific region near the analyzer crystal, allowing the simultaneous acquisition of transmitted and diffracted images in a single exposure. When combined with computed tomography, three different sample properties, known as absorption, phase and scattering, can be reconstructed simultaneously by collecting the projective images as the sample rotates from 0° to 360°. The experimental results demonstrate that this straightforward method enables the quantitative extraction of sample information and simplifies the data acquisition procedure in computed tomography with diffraction enhanced imaging. Therefore, this novel method offers the advantages of straightforward imaging device, rapid CT data acquisition, low radiation dose and more comprehensive sample information extraction.