By using first-principles method, we study the stacking effects on the electronic structure, topological phase and spin splitting in the bulk and film of topological insulator Bi2Se3. It is found that the different stackings can lead to different interlayer interactions and change the centrosymmetry of Bi2Se3. The centrosymmetric ABC and AAA stackings in bulk Bi2Se3 have similar band structures. ABA stacking breaks the centrosymmetry, giving rise to considerable changes of the band structure and large spin splitting. We further study the stacking effects in the film of Bi2Se3 and find that the non-centrosymmetric ABA stacking can induce large spin splitting in Bi2Se3 film. It is proposed and illustrated that the strain can tune the spin splitting effectively.