  We report the superconductivity at Tc ~ 0.049 K in Laves phase HfZn2. Based
on the first principles method we have studied the details structural and
electronic properties of HfZn2 according to which there are 4.67 states eV-1
fu-1 at Fermi level. Using this value we calculate the specific heat
coefficient {\gamma} theoretically as 10.97 mJ/ K2 mol and then systematically
calculate the electron-phonon coupling constant {\lambda} as 0.45. Finally
applying these values in McMillan formula we get the superconducting critical
temperature of HfZn2 as approximately 0.049 K.
