Film cooling technology is widely used in gas turbines. With the additive manufacturing anticipated in the future, there will be more freedom in film cooling hole design. Exploiting this freedom, the present authors tried using curved holes to generate Dean vortices within the delivery line. These vortices have opposite direction of rotation to the vorticity of the kidney vortices and, thus, there is interaction between these vortices in the mixing region. It is shown that as a result of the inclusion of Dean vortices, the curved hole delivery leads to enhanced film cooling effectiveness. Numerical results, including film cooling effectiveness values, tracking of vortices in the flow field, heat transfer coefficients, and net heat flux reduction (NHFR), are compared between the curved hole, round hole, and a laidback, fan-shaped hole with blowing ratios, M, of 0.5, 1.0, 1.5, 2.0, and 2.5. The comparison shows that film cooling effectiveness values with the curved hole are higher than those with cylindrical film cooling holes at every blowing ratio studied. The curved hole has lower film cooling effectiveness values than the laidback, fan-shaped holes when M = 0.5 and 1.0, but shows advantages when the blowing ratio is higher than 1.0. There is heat transfer enhancement for the curved hole case due to a higher kinetic energy transferred to the near-wall region, however. Nevertheless, the curved hole still displays a higher NHFR when the blowing ratio is high.