In this paper, we establish a theoretical model of reciprocal-lattice vector of the two-dimensional hexagonal phase array optical beam splitter modulated by an external electric field, perform the analysis of the tunable phase-difference array optical beam splitter according to the numerical simulation, and then obtain the images of intensity distribution with different values of fractional Talbot distance and external electric field. The two-dimensional hexagonal phase array optical beam splitter is designed and fabricated by lithium niobate. An experimental study of beam splitting is also given. When the applied voltage is 0.5 kV (with electric field of 1 kV/mm), we observe the phenomenon of the beam splitting in Talbot diffraction. As the external field increases, the images of beam splitting in diffraction become clearer, the experimental results are in agreement with theoretical results.