X-ray luminescence computed tomography (XLCT) is an emerging hybrid imaging modality, which is able to improve the spatial resolution of optical imaging to hundreds of micrometers for deep targets by using superfine X-ray pencil beams. However, due to the low X-ray photon utilization efficiency in a single pinhole collimator based XLCT, it takes a long time to acquire measurement data. Herein, we propose a multiple pinhole collimator based XLCT, in which multiple X-ray beams are generated to scan a sample at multiple positions simultaneously. Compared with the single pinhole based XLCT, the multiple X-ray beam scanning method requires much less measurement time. Numerical simulations and phantom experiments have been performed to demonstrate the feasibility of the multiple X-ray beam scanning method. In one numerical simulation, we used four X-ray beams to scan a cylindrical object with 6 deeply embedded targets. With measurements from 6 angular projections, all 6 targets have been reconstructed successfully. In the phantom experiment, we generated two X-ray pencil beams with a collimator manufactured in-house. Two capillary targets with 0.6 mm edgeto-edge distance embedded in a cylindrical phantom have been reconstructed successfully. With the two beam scanning, we reduced the data acquisition time by 50%. From the reconstructed XLCT images, we found that the Dice similarity of targets is 85.11% and the distance error between two targets is less than 3%. We have measured the radiation dose during XLCT scan and found that the radiation dose, 1.475 mSv, is in the range of a typical CT scan. We have measured the changes of the collimated X-ray beam size and intensity at different distances from the collimator. We have also studied the effects of beam size and intensity in the reconstruction of XLCT.