Based on first-principles calculations in the framework of van der Waals density functional theory, we find that giant Rashba-like spin splittings can be induced in both the surface states and quantum well states of thin Bi2Se3 films by application of an external electric field E.The charge is redistributed so that the Dirac cones of the upper and lower surfaces become nondegenerate and completely gapless.Interestingly, a momentum dependent spin texture is developed on the two surfaces of the films.Some of the quantum well states, which reside in the middle of the Bi2Se3 film under zero field, are driven to the surface by the electric field.The Rashba splitting energy has a highly nonlinear dependence on the momentum and the electric field due to large contribution of the high-order Rashba terms, suggesting a complex spin dynamics in the thin films of Bi2Se3 under electric field.