The simultaneous dual-band pulsed amplification is demonstrated from an Er/Yb co-doped fiber (EYDF), and consequently a high-power all-fiber single-mode 1.0/1.5 μm dual-band pulsed master oscillator power amplifier (MOPA) laser source is realized for the first time, to the best of our knowledge, based on one singlegain fiber. The simultaneous outputs at 1061 and 1548 nm of the laser source have the maximum powers of 10.7 and 25.8 W with the pulse widths of 9.5 ps and 2 ns and the pulse repetition rates of 178 and 25 MHz, respectively. This EYDF MOPA laser source is seeded by two separate preamplifier chains operating at 1.0 and 1.5 μm wavebands. The dependence of the laser output powers on the length of the large-mode area EYDF, the ratio of the powers of the two signals launched into the booster amplifier, and the wavelength of the 1 μm seed signal are also investigated experimentally.