V-band high-speed CCD photometry of V 1028 Cyg revealed that hump structures existed in the early stage of its 1995 July outburst. We obtained 0.06154 (+/- 0.00002) d as the best estimated period of superhumps. We confirmed that this dwarf nova belongs to the SU UMa stars. A re-brightening occurred after the superoutburst, and may be associated with a normal outburst. An analysis of the timings of superhump maxima showed clear evidence for an increase of the superhump period (P_dot = .P/P) with 7.54 x 10-6. Only a few stars (AL Com, T Leo, SW UMa, etc.) are reported to have such an increase of the superhump period. At the end of the superoutburst, we detected that the amplitude of the superhumps increased considerably. Both of these properties are not typical features of ordinary SU UMa stars. The connection between the WZ Sge-type and the SU UMa-type dwarf novae is briefly discussed.