As a prominent three-dimensional (3-D) topological insulator, traditional thermoelectric material Bi2Te3 has re-attracted greater interest in recent years. Herein, we demonstrate for the first time that c-axis oriented strained Bi2Te3 films exhibit the bulk photovoltaic effect (BPVE) at infrared wavelengths, which was only found in wide band-gap ferroelectric materials before. Moreover, further experiments show that the bulk photovoltaic effect probably comes from the flexoelectric effect which was induced by the stress gradient in strained Bi2Te3 films. And we anticipate that the results are generalizable to other layer-structured or two-dimensional (2-D) materials, e.g., Bi2Se3 and MoS2.