Using cosmological particle hydrodynamical simulations and uniform ultraviolet background, we test Lyman-alpha forest flux spectra predicted by the conventional cold dark matter (CDM) model, the free-particle wave dark matter (FPpsiDM) model and extreme-axion wave dark matter (EApsiDM) models of different initial axion field angles against the BOSS Lyman-alpha forest absorption spectra. The boson mass mb of all DM models is fixed to mb ~ 10^-22eV. We recover the results reported previously [17, 1] that the CDM model agrees better with the BOSS data than the FPpsiDM model by a large margin, where the difference of total chi-square is 19 for 420 data bins. These previous results demand a larger boson mass by a factor > 10 and are in tension with the favoured value. However, we find this tension can be alleviated as a range of EA DM models predict Lyman- flux spectra agree better with the BOSS data than the CDM prediction by an even larger margin; the difference of total chi-square can be as large as 24. This finding is perhaps not surprising since EA DM models can have a unique spectral bump in excess of the power of CDM near the more extended spectral cutoff in the initial matter power spectrum [51, 50].