The purpose of this work is to introduce and study a novel x-ray beam irradiation pattern for X-ray Luminescence Computed Tomography (XLCT), termed multiple intensity-weighted narrow-beam irradiation. The proposed XLCT imaging method is studied through simulations of x-ray and diffuse lights propagation. The emitted optical photons from X-ray excitable nanophosphors were collected by optical fiber bundles from the right-side surface of the phantom. The implementation of image reconstruction is based on the simulated measurements from 6 or 12 angular projections in terms of 3 or 5 x-ray beams scanning mode. The proposed XLCT imaging method is compared against the constant intensity weighted narrow-beam XLCT. From the reconstructed XLCT images, we found that the Dice similarity and quantitative ratio of targets have a certain degree of improvement. The results demonstrated that the proposed method can offer simultaneously high image quality and fast image acquisition.