Directional speech enhancement of signals from microphone arrays is an effective way to improve speech recognition for cochlear implant users. The strict implant size limitation results in a short distance between microphones. The fractional delay problem due to the short distance between microphones is solved by a maximal flat (Maxflat) finite impulse response (FIR) filter, using the Maxflat error criteria at a low frequency containing most of the speech information and energy. The fractional Maxfiat FIR filter approximates the ideal digital fractional filter at the magnitude response, phase response, and phase delay characteristics, and is also very low order. The results demonstrate that the Maxfiat FIR filter accurately and effectively solves the fractional digital delay and is very suitable for real-time speech processing in practical cochlear implant products.