We present a detailed investigation of the Doppler shift oscillations in a hot loop during an M7.1 flare on 2014 October 27 observed by the Interface Region Imaging Spectrograph. The periodic oscillations are observed in the Doppler shift of Fe XXI 1354.09Å (logT ∼7.05), and the dominant period is about 3.1 minutes. However, such 3.1-min oscillations are not found in the line-integrated intensity of Fe XXI 1354.09Å, AIA EUV fluxes, or microwave emissions. SDO/AIA and Hinode/XRT imaging observations indicate that the Doppler shift oscillations locate at the hot loop-top region (≥11 MK). Moreover, the differential emission measure (DEM) results show that the temperature is increasing rapidly when the Doppler shift oscillates, but the number density does not exhibit the corresponding increases nor oscillations, implying that the flare loop is likely to oscillate in an incompressible mode. All these facts suggest that the Doppler shift oscillations at the shorter period are most likely the standing kink oscillations in a flare loop. Meanwhile, a longer period of about 10 minutes is identified in the time series of Doppler shift and line-integrated intensity, GOES SXR fluxes and AIA EUV light curves, indicating the periodic energy release in this flare, which may be caused by a slow mode wave.