Broadband near-to-shot-noise suppression of the intensity noise from a continuous-wave (cw) fiber laser at 1550 nm is demonstrated at GHz-frequencies using feed-forward phase-matched destructive noise interference impressed onto the optical signal with a fiber electro-optic power modulator. The scheme is independent of the laser frequency and therefore is suitable for tunable lasers. It can be used with some modifications after an optical fiber-amplifier boosting a cw laser signal. A noise residual of down to 2 dB above the shot-noise was measured, which is about 2 dB below the prediction with a rigorous noise model. While the total laser noise can be removed, inclusive shot noise, because the latter is still 10 dB above the thermal noise, the power splitter introduces some partition noise above the shot level. In that case, a sub-shot-noise suppression scheme should be possible by replacing the photon anti-correlation of the power splitter by the co-correlation obtained from a paired photon or twin beam source.