Leading-edge multi-channel double-wall design, a novel internal cooling structure, has been presented recently to enable higher overall cooling effectiveness with less penalty of coolant and pressure loss. Our previous work has proved the advantages of the design under operating condition relative to conventional internal cooling methods, including impingement cooling and swirl cooling. Channel impingement cooling structure, which is utilized at the turning region of the leading edge, is the critical factor to realize the high cooling performance of the design. Hence, the turning angle and turning internal radius of the cooling channel are two key parameters for the novel design, and this paper focuses on the effects of these two parameters on the flow and heat transfer characteristics of the design. Nine simplified single-channel models with different turning angles (45 deg, 60 deg, and 75 deg) and radii (0.6 mm, 0.9 mm, and 1.2 mm) were adopted to conduct the study, and the jet Reynolds number ranges from 10,000 to 40,000. The results show that the turning angle and turning internal radius affect the jet form significantly for the same mechanism. Small turning angle means large impingement, which leads to stream-wise counter-rotational vortices and high turbulence intensity, but increasing turning internal radius transfers the jet form from impingement jet to laminar layer attaching the target surface with low heat transfer. The turning internal radius has stronger effect than turning angle. With higher jet Reynolds number, both the heat transfer and total pressure loss increase dramatically, and the effects of geometrical parameters are clearer.