  The hypothetical axion and axion-like particles, feebly coupled with photon,
have not yet been found in any experiment. With the improvement of laser
technique, much stronger but shorter quasi-static electric and magnetic fields
can be created in laboratory using laser-plasma interaction, compared to the
fields of large magnets, to help the search of axion. In this article, we
discuss the feasibility of ALPs exploration using planarly or cylindrically
symmetric laser-plasma fields as background and an x-ray free-electron laser as
probe. Both the probe and the background fields are polarized such that the
existence of ALPs in the corresponding parameter space will cause polarization
rotation of the probe, which can be detected with high accuracy. Besides, a
structured field in the plasma creates a tunable transverse profile for the
interaction and improves the signal-to-noise ratio via phase-matching
mechanism. The ALP mass discussed in this article ranges from $10^{-3}$ eV to 1
keV. Some simple schemes and estimations on ALP production and polarization
rotation of probe photon are given, which reveals the possibility of future
laser-plasma ALP source in laboratory.
