In this study evaluated the overall characteristics of turbulent flow and turbulent premixed flame of a circular fractal turbulence generator in a V-shaped flame. Cross and square types were used for the fractal pattern type, and the main shape parameters, blockage ratio and thickness reduction ratio, were = 30, 40, 50 %, = 0.4, 0.6, 0.8, 1.0, respectively, and the number of iterations N was fixed at 3. And a hexa type, a perforated plate with the same blockage ratio, was also manufactured for comparison. First, the characteristics of the non-reactive turbulent flow that directly affect the turbulent premixed flame were confirmed. Through the results of the central axis turbulence flow, the turbulence increasing effect of the fractal turbulence generator was quantitatively confirmed, and the maximum turbulence intensity was expressed as a predictable correlation equation as a shape parameter of the fractal turbulence generator. The turbulent flow non-uniformity of the fractal turbulence generator was statistically evaluated from the results of the 2D planar turbulent flow. The structure of a V-shaped turbulent premixed flame and two turbulent burning velocities (turbulent local displacement velocity and turbulent local consumption velocity) were calculated using the OH_PLIF image. It was confirmed that the thickness and angle of the flame brush derived from the mean progress variable were different for each turbulence generator, and the thickness of the flame brush was also expressed as a correlation between the shape parameters of the fractal turbulence generator. It was statistically shown that the local displacement speed and local consumption speed increased significantly compared to the general perforated plate and mesh type. It was confirmed that the two turbulent burning velocities are expressed by the correlation equation of the turbulent flow factors (velocity fluctuation and integral length scale). As a new approach, a correlation equation was proposed for the two turbulent burning velocities expressed as shape parameters of a fractal turbulence generator. The results of this study provide a tool to predict in advance the characteristics of turbulent flow and turbulent flame in the design process of [fundamental study or industrial combustion system] using a turbulence generator.