We have generated the second, third, fourth, and fifth harmonics of the output of a Yb-doped fiber amplifier seeded by a passively Q-switched Nd:YAG microchip laser. The fiber amplifier employed multimode fiber (25 μm core diameter, V ~ 7.4) to provide high-peak-power pulses, but diffraction-limited beam quality was obtained by use of bend-loss-induced mode filtering. The amplifier output had a pulse duration of 0.97 ns and smooth, transform-limited temporal and spectral profiles (~500 MHz linewidth). We obtained high nonlinear conversion efficiencies using a simple optical arrangement and critically phase-matched crystals. Starting with 320 mW of average power at 1064 nm (86 µJ per pulse at a 3.7 kHz repetition rate), we generated 160 mW at 532 nm, 38 mW at 355 nm, 69 mW at 266 nm, and 18 mW at 213 nm. The experimental results are in excellent agreement with calculations. Significantly higher visible and UV powers will be possible by operating the fiber amplifier at higher repetition rates and pulse energies and by further optimizing the nonlinear conversion scheme.