Dielectric laser acceleration (DLA) is new cheap and miniature laser acceleration scheme for acceleration of charged particles in the vicinity of the dielectric grating. In this paper injection characteristics of the electron bunch in a single fused silica grating based-structure with period λg=260 nm is analyzed. Optimum aspect ratios of the grating width d/λg and height h/λg are obtained for the first surface mode harmonic. Simulation results of the injected electron dynamics show that there are two lateral positions (y=1.75 and y=2.6 μm) that the final electron energy is maximized. Existence of these two lateral positions increases flexibility of the injection process. In other words, injection can be made in the range of 1.4 < y(μm)<2.8 with two peaks of energy. Finally, injection of Gaussian electron bunch at each two optimum transverse positions is investigated by a numerical simulation. The initial momentum distribution is assumed to be Gaussian around the mean resonance velocity (β=λg/λ=0.33). The initial longitudinal and transverse emittance of the electron bunch are selected as ε||=(δE/E)=0.01 and, ε⊥=3μmmrad respectively. The net energy gain in the fifty grating periods is 2.03 keV (2.225 keV) and acceleration gradient for each injection position is about 160 MeV/m.