We have studied the effect of tensile strain on the superconductivity in FeSe films. 50 nm, 100 nm, and 200 nm FeSe films were grown on MgO, SrTiO$_3$, and LaAlO$_3$ substrates by using a pulsed laser deposition technique. X-ray diffraction analysis showed that the tetragonal phase is dominant in all of our FeSe films. The 50 nm FeSe films on MgO and SrTiO$_3$ are under tensile strain, while the 50 nm FeSe film on LaAlO$_3$ and the other thick FeSe films are unstrained. Superconducting transitions have been observed in unstrained FeSe films with T$_{onset}$ $approx$ 8 K, which is close to the bulk value. However, no sign of superconductivity has been observed in FeSe films under tensile strain down to 5 K. There is evidence to show that tensile strain suppresses superconductivity in FeSe films.