We design and experimentally demonstrate a few-mode Raman amplifier over the C+L band with a flat on-off gain of ∼4 dB, for the first time, to the best of our knowledge. A state-of-the-art gain bandwidth of 75 nm (1530-1605 nm) is achieved. The wavelength-dependent gain for both LP01 and LP11 modes is about 0.6 dB, and the maximum mode-dependent gain is less than 0.3 dB. Mode-division multiplexed optical transmissions are performed over 75 km few-mode fiber assisted by the proposed Raman amplifier. Due to the low noise Raman amplification, more than 3.3 dB optical signal-to-noise ratio enhancement has been obtained with a significantly improved bit-error rate of about two orders.