We study five Luminous Blue Variable (LBV) candidates in the Andromeda galaxy and one more (MN112) in the Milky Way. We obtain the same-epoch near-infrared (NIR) and optical spectra on the 3.5-meter telescope at the Apache Point Observatory and on the 6-meter telescope of the SAO RAS. The candidates show typical LBV features in their spectra: broad and strong hydrogen lines, HeI, FeII, and [FeII] lines. We estimate the temperatures, reddening, radii and luminosities of the stars using their spectral energy distributions. Bolometric luminosities of the candidates are similar to those of known LBV stars in the Andromeda galaxy. One candidate, J004341.84+411112.0, demonstrates photometric variability (about 0.27 mag in V band), which allows us to classify it as a LBV. The star J004415.04+420156.2 shows characteristics typical for B[e]-supergiants. The star J004411.36+413257.2 is classified as FeII star. We confirm that the stars J004621.08+421308.2 and J004507.65+413740.8 are warm hypergiants. We for the first time obtain NIR spectrum of the Galactic LBV candidate MN112. We use both optical and NIR spectra of MN112 for comparison with similar stars in M31 and notice identical spectra and the same temperature in the J004341.84+411112.0. This allows us to confirm that MN112 is a LBV, which should show its brightness variability in longer time span observations.