In FIR (Finite Impulse Response) filter applications, Nth-band FIR digital filters are known to be important due to their reduced computational requirements. The conventional methods for designing FIR filters use iterative approaches such as the well-known Parks-Mcclellan algorithm. the Parks-Mcclellan algorithm is also used to design Nth-band FIR digital filters. But a disadvantage of the Parks-McClellan algorithm Is that it needs a good amount of design time. This paper describes a direct design method for third-band FIR Filters using Chebyshev polynomial, which provide a reduction in design time over indirect methods such as the Parks-McClellan algorithm. The response of the resulting filter is equi-ripple in passband. The proposed method of design produces a passband response that is equi-ripple to within a minuscule error, compare to that of the Parks-McClellan algorithm.