We report the discovery of a giant planet in the KMT-2016-BLG-1397 microlensing event, which was found by The Korea Microlensing Telescope Network alone. The timescale of this event is tE = 40.0 ± 0.5 days, and the mass ratio between the lens star and its companion is q = 0.016 ± 0.002. The planetary perturbation in the light curve is a smooth bump, resulting in the classical binary-lens/binary-source (2L1S/1L2S) degeneracy. We measure the V − I color of the (putative) two sources in the 1L2S model, and then effectively rule out the binary-source solution. The finite-source effect is marginally detected. Combined with the limits on the blend flux and the probability distribution of the source size normalized by the Einstein radius ρ, a Bayesian analysis yields the lens mass M_L = 0.45^(+0.33)_(-0.28) M⊙, at distance of D_L = 6.60^(+1.10)_(-1.30) kpc. Thus, the companion is a super-Jupiter of a mass m_p = 7.0^(+5.2)_(-4.3) M_J, at a projected separation r_⊥ = 5.1^(+1.5)_(-1.7) au, indicating that the planet is well beyond the snow line of the host star
