In this letter, we first propose quantum teleportation protocols to teleport a Greenberger–Horne–Zeilinger state and a W state via Brown state quantum channel. We find the orthogonal basis onto which Alice projects her states by quantum Fourier transforming her quantum states. According to the principle of quantum mechanics, we calculate the unitary operations Bob needs to perform to recover the teleportated states. Then, we generalize our protocols in a multi-qubit system. We show that our scheme can be easily extended to a multi-qubit system. Our method of using quantum Fourier transform to find the projective basis is universal and convenient, and it could have potential use in quantum communication.