The initial texture effect of strain rate sensitivity response in magnesium alloys was studied using the quasi in situ electron backscatter diffraction technique. The strain accumulations, under uniaxial loading of both tensile and compression along the rolling direction, showed strain rate dependency. For the AZ31 magnesium sheets with strong basal texture (max intensity to 11.2), twinning first occurs at the onset of plastic deformation, resulting in macroscopic strain rate insensitivity. With further loading, the strain rate sensitivity significantly increases (with the strain rate sensitivity coefficient m increased from 0.0025 to 0.012), arising from the initiation of slip. For the WE43 alloy sheets with weak basal texture (max intensity to 2.6), the overall deformation is sensitive to strain rate under both tensile and compression. The twinning growth rate and twinned volume fraction have been used to identify whether the process is twin-dominated or slip-dominated during the plastic deformation of a magnesium alloy.