With the density of function with pesudopotentional and plane-wave method, we study the strain effect on band structure of multi-layered BN film. It is found that the band gap of BN film decreases linearly with the increase of tensile strain, and the slope of the band gap-strain curve is independent of the BN stacking and the number of the BN layers, indicating that the band structure of BN film is determined by the interlayer interaction rather than the intralayer interaction.