A high-power transverse-mode-switchable all-fiber picosecond laser in a master-oscillator power-amplifier (MOPA) configuration is demonstrated. The master oscillator is a gain-switched laser diode delivering picosecond pulses with 25 MHz repetition rate at the wavelength of 1.06 μm. After multi-stage amplification in ytterbium-doped fibers, the average output power is scaled to 117 W. A mechanical long-period grating is employed as a fiber mode convertor to achieve controllable conversion from the fundamental (LP01) to the second-order (LP11) mode. Efficient mode conversion is demonstrated and the output characteristics for both modes are investigated. It is shown that LP01 and LP11 modes have nearly identical optical-to-optical conversion efficiency during amplification, but the nonlinear spectral degradation is significantly alleviated for LP11 mode operation. Owing to the compact all-fiber architecture, this high-power transverse-mode-switchable fiber laser is reliable during long-term operation and thus promising for many practical applications, e.g. high-resolution laser micro-processing.