We report the kinematic shift of C IV broad absorption line (BAL) in quasar SDSS J120819.29+035559.4 (hereafter J1208+0355). This quasar shows two BAL systems, including a blue component of system A at ∼ 23500 km s −1 that shows kinematic shift of 1166±65 km s −1 , and a red component of system B at ∼ 7000 km s −1 that can be decomposed into several narrow absorption lines (NALs). First, we confirm that the most likely cause for the equivalent width variations of the absorption lines (at least for sysetm B) in J1208+0355 is ionization change scenario as response to the changes in the ionization continuum according to the following observational factors: (1) coordinated multiple absorption lines strengthening; (2) the continuum flux shows an obvious weakening. Secondly, we find line-locking phenomena from the blended NALs within system B, indicating that these outflow clouds are driven by radiative force caused by resonance lines. The above two research aspects convincingly reveal that the BAL outflows of J1208+0355 are affected by the background radiation energy. Therefore, we infer that the kinematic shift shown in system A may be produced by actual line-of-sight acceleration of the outflow clouds, which is driven by radiation pressure from the background light source.