MgZnO becomes amorphous or short-range-ordered with the addition of hafnium oxide. The films are rf-sputter deposited onto glass substrates (Eagle 2000, Corning Inc.) from Mg0.05HfxZn0.95-xO targets (x=0, 0.025, 0.05, 0.075, 0.1) in pure Ar ambient at room temperature. The sputtered Mg0.05Zn0.95O exhibits strong (002) preferred orientation with XRD peak located at 2θ=34.16o. The XRD peak intensity is also greatly reduced, indicating the material amorphorization proceeds with the addition of Hf. The grain size, estimated from the full-width-at-half-maximum (FWHM) of the (002) XRD peak, decreases from 24.1 to 3.3 nm as the Hf content x increases from 0 to 0.025 in Mg0.05HfxZn0.95-xO. No sharp XRD peaks are detected in the as-sputtered films when more than 5.0 at.% Hf are added into the materials. The films remain in amorphous or short-range-ordered states after annealing at 600 oC for 30 mins. All Mg0.05HfxZn0.95-xO films (100 nm in thickness) are highly transparent (> 80 %) in the visible region from 400 to 800 nm and have sharp absorption edges in the UV region. The tauc bandgap ΔE (eV), as a function of hafnium composition x, is fitted as ΔE=3.336+6.08x for room temperature as-deposited films, and ΔE=3.302+2.60x for films after 30 min 600 oC annealing. The annealing process decreases the bandgap shift caused by the incorporation of Hf in the materials.