Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) onboard the Solar Orbiter, we statistical investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region, i.e., NOAA 12965. A total of 111 coronal loops are identified in EUI 174 ˚A images, and they all reveal transverse oscillations without any significant decaying, regarding as decayless oscillations. Oscillatory periods are measured from ∼11 s to ∼185 s, with a median period of 40 s. Thus, they are also termed as short-period oscillations. The corresponding loop lengths are measured from ∼10.5 Mm to ∼30.2 Mm, and a strong dependence of oscillatory periods on loop lengths is established, indicating that the short-period oscillations are standing kinkmode waves in nature. Based on the coronal seismology, kink speeds are measured to ∼330−1910 km s−1 , and magnetic field strengths in coronal loops are estimated to about 4.1−25.2 G, while the energy flux carried by decayless kink oscillations lies in the range from roughly 7 W m−2 to 9220 W m−2 . Our estimations suggest that the wave energy carried by short-period decayless kink oscillations can not support the coronal heating in the active region.