8 types of maximally flat FIR fractional delay filters are proposed. They are designed by separately approximating the real part and the imaginary part of the frequency response. Among these 8 types of filters, two of them are equivalent to the existing design results in the open literature (Samadi, 2004). Therefore, a more general closed-form design of the maximally flat FIR fractional delay filters is described in this paper and some design examples of FIR fractional delay filters are illustrated.