  For space gravitational wave (GW) detection, arm locking is a proposal useful
in decreasing the frequency noise of the laser sources for current developing
space missions LISA and TAIJI/TIANQIN. In this paper, we study the application
of arm locking to the Astronomical Middle-frequency Interferometric
Gravitational Observatory (AMIGO) to decrease the frequency noise of laser
sources. For AMIGO, the arm-locking technique can suppress the laser frequency
noise by three orders of magnitude. The advantage of this is to make the
auxiliary noise assignment for AMIGO easier and more relaxed. For the
first-generation time-delay interferometry (TDI) configuration, the laser
frequency noise contribution is already below the core noise contribution. For
the simple Michelson TDI configuration (X0), the arm locking makes the
acceleration-thrust scheme, the delay-line scheme, or the combined scheme
easier to implement. Within a relatively short period of less than a day
(compared to less than twenty days for LISA/TAIJI), the Doppler frequency
pulling can be efficiently reduced to within $\pm$ 0.001 Hz and does not affect
the mission duty cycle much.
