Abstract: To find a solution for the high brightness, ultra-short pulse X-ray source, the betatron X-ray mechanism was studied. It is based on the interactions which generate the laser wake field acceleration (LWFA), between the ultra-intense short laser and the plasma. These accelerated electrons make betatron oscillations in the transverse fields of the bubble and emit high brightness and ultra-short X-ray pulses (about fs). Also, this kind of source has the advantages of small size, low cost. The numerical calculations of the emission of the betatron X-rays were carried out with 2D-PIC simulations and the data processing software. Synchrotron spectra with critical energy of 3 keV and 10 keV which are radiated by the lower energy electrons (about 100 MeV) and the higher energy electrons (about 170 MeV) respectively, are reported and the emission is confined to a small angle of about 8 mrad, which has a good agreement with the theoretical results.