Based on thin film optics (TFO) and finite element method (FEM), we have theoretically investigated improving external quantum efficiency (EQE) by anti-reflection (AR) films constructed from subwavelength nano multi-layers (NML) of low and high index materials, where the low and high index materials are MgF2 and Ta2O5, respectively. This kind of NML dielectric structures have the advantages of low-cost and flexible. Three kinds of substrates have been studied here, which are glass, polyethylene naphthalate (PEN), and polyethylene terephthalate (PET), respectively. TFO theory has been used to obtain the transmittance and reflectance, which agrees well with FEM results. For NML structure, TFO is more efficient than FEM in terms of calculation time and accuracy. The average AR effects (AAREs) are about 3.69%, 3.46% and 3.07% on glass substrate, about 6.15%, 5.56% and 5.02% on PEN substrate, and about 5.06%, 4.62% and 4.17% on PET substrate, for AR bands (ARBs) 350~800 nm, 350~1100 nm and 350~1500 nm, respectively. The results also reflect that wider AR bandwidth needs more NML layers. In practice, this kind of AR films can be widely applicable to enhance the EQE of the optoelectronic devices (OEDs). INDEX TERMS Anti-reflection, nano multi-layers, thin film optics, finite element method.