We demonstrate the operation of a CW multi-wavelength erbium-doped fiber laser covering the whole C-band. The laser system consists of a frequency-shifted ring cavity with a new type of periodic filter, namely a fiber Bragg grating array. Careful control of the individual grating strength has allowed us to obtain 17 laser lines, from 1527 to 1562 nm, with output flatness better than 3 dB. We also report on the optimization and characterization of the CW laser emission.