A diode-pumped Yb-doped double-clad fiber amplifier (YDDCFA) with the narrow bandwidth continuous wave (CW) and pulse input signal is investigated. The input single-mode (SM) signal bandwidth is 10^(-4) nm from a distributed feedback (DFB) fiber laser. The saturated gain of the CW amplification is 11 dB at the forward pump. And besides CW signals, we also amplify pulses with duration of 150 ns and the 1-Hz repetition. The pulse is amplified to 2 W of peak power, 0.31 microjoule of energy, 23 dB of gain and less than 6% of stability at the forward pump power of 1.4 W. For higher power, reflections and backscattering can generate the self pulsation in the amplifier. The results are important for the development of the narrow-band double-clad fiber amplifier.