In this paper, we study light-driven bending vibration of a liquid crystal elastomer (LCE) beam. Inhomogeneous and time-dependent number fraction of photochromic liquid crystal molecules in cis state in an LCE beam is considered in our model. Using mode superposition method, we obtain semi-analytic form of light-driven bending vibration of the LCE beam. Our results show that periodic vibration or a statically deformed state can be induced by a static light source in the LCE beam, which depends on the light intensity and position of the light source. We also demonstrate that the amplitude of the bending vibration of the LCE beam can be regulated by tuning light intensity, damping factor of the beam, and thermal relaxation time from cis to trans state, while the frequency of the vibration in the beam mainly depends on the thermal relaxation time. The method developed in the paper can be important for designing light-driven motion structures and photomechanical energy conversion systems.