Both dynamic mechanisms and diffraction characteristics of the local volume photorefractive holographic gratings recorded by two finite bounded plane waves in doubly doped LiNbO3:Fe:Mn crystals are investigated, by taking into account both the band transport model and two-dimensional coupled-wave theory. The three step method is used to solve both the band transport equation and the two-dimensional coupling equation. The numerical calculations show that the spatial distribution of the space-charge field is non-homogeneous in the local volume photorefractive holographic gratings. The space-charge field is much stronger when the grating region is smaller. As the grating region widening, the space-charge field decreases by an order of magnitude. Besides, the time-space variation of the space-charge field is the same as that of one dimension infinite photorefractive holographic gratings in the place closer to the incident boundary. But the influence of the special local effect on the space-charge field is very important as the grating region extends. It is also shown that the diffraction efficiency increases with the increase of the grating length of the local volume photorefractive holographic gratings. The theoretical results provide valuable insight to the design and application of these gratings and the finite boundary photorefractive holographic optical elements.