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.