This paper studies fast algorithm for implementing the multiplier-less discrete cosine transform and discrete sine transform required in the linear-phase cosine-modulated filter banks (LP-CMFB). It is shown that the modulation involves both the type-I discrete cosine transform (DCT-I) and discrete sine transform (DST-I) of the same sequence, which can be computed together via a real-valued discrete Fourier transform (DFT) and a real-valued odd-DFT. This in turn can be computed by fast Fourier transform (FFT) algorithm of appropriate length. The resulting algorithm is very efficient, highly regular and supports wide range of transform lengths. Using the proposed algorithm and a new multiplier-less FFT-like transformation, multiplier-less realization of the LP-CMFB is obtained. Its arithmetic complexity is analyzed and an example is given to illustrate the principle of-the proposed algorithm.