Solid carbide cylindrical end-mills are widely used in machining, and their helical flutes are crucial to their cutting performance. In industry, the flute is simply defined with four key parameters: the helical angle, the radial rake angle, the fluting angle, and the core radius, which are specified in an end-mill design. The flute shape is not fully defined, while it is often generated by a 1A1 or 1V1 diamond wheel in 2½-axis computer numerically controlled (CNC) grinding. Unfortunately, the two simple wheels cannot make largely different flute shapes, preventing further improvement of the end-mills. Although no research result on how the flute geometry affects the end-mill cutting attribute has come into public yet, it is now necessary to employ more complicated wheels to grind flutes with the specified parameter values but much different flute shapes. For this purpose, the 4Y1 diamond wheel is employed in this work. However, the commercial tool grinding software cannot determine the dimensions and the set-up angle for the 4Y1 wheel. To address this problem, a new mathematical model of the flute parameters in terms of the dimensions and the set-up angle of the 4Y1 wheel is formulated, thus, the 4Y1 wheel can be used in flute grinding. This work lays a foundation of using complex wheels to grind flutes with more shapes in order to improve the end-mill's cutting ability.