We present the results obtained from the UV photometry of the globular cluster NGC 1261 using Far-UV (FUV) and Near-UV (NUV) images acquired with the Ultraviolet Imaging Telescope (UVIT) onboard the Astrosat satellite. We utilized the UVIT data combined with HST, GAIA, and ground-based optical photometric data to construct the different UV colour-magnitude diagrams (CMDs). We detected blue HB (BHB), and two extreme HB (EHB) stars in FUV, whereas full HB, i.e., red HB (RHB), BHB as well as EHB is detected in NUV CMDs. The 2 EHB stars, identified in both NUV and FUV, are confirmed members of the cluster. The HB stars form a tight sequence in UV-optical CMDs, which is almost aligned with Padova isochrones. This study sheds light on the significance of UV imaging to probe the HB morphology in GCs.