As a purpose of developing micro-actuators driven by liquid crystals, transient behaviors of a nematic liquid crystal between two parallel plates under an electric field have been investigated numerically by using the Leslie-Ericksen theory as a constitutive equation. Applied voltage, gap of the plates, and twist and tilt angles have been selected as computational parameters. We have used the Crank-Nicolson method for the time integration, and a finite difference method for spatial discretization. The material constants, such as viscosity coefficients, elastic constants, and dielectric constants of 5CB (4-n-pentyl-4'- cyano-biphenyl) have been employed in this computation. Imposition of an electric field on a liquid crystal induces flow (so called back-flow), whose profile and magnitude depend strongly on the twist angle of the director; when the twist angle is 0 deg, the induced flow is planar and the velocity profile between plates is S-shaped and anti-symmetric with respect to the center plane of the two plates. With increasing the twist angle, the flow has an out of plane component, and finally the profile becomes unidirectional when the twist angle reaches 180 deg. With the increment of the applied voltage, the shear stress acting on the plate, the velocity, and the flow rate are increased and the response is improved. The effect of the gap of the plates is large; when the gap is reduced to 5 μm, for example, the response is so high that the physical quantities become maxima within a couple of milliseconds. However, if the electric field intensity is kept constant, the effect of the gap is negligible. The tilt angle has comparatively little effect. It is found from the results obtained in this study that liquid crystalline micro-actuators with arbitrary characteristics can be developed by controlling properly applied voltage, size of actuators, and anchoring conditions.