We performed spectroscopy of five Luminous Blue Variable (LBV) candidates and two known LBV stars (AE And and Var A-1) in M31. We obtained the same-epoch near-infrared (NIR) and optical spectra of these stars. The NIR spectra were taken with Triplespec spectrograph at the 3.5-m telescope at Apache Point Observatory, and the optical spectroscopy was done with SCORPIO focal reducer at the 6-m BTA telescope (SAO RAS). The candidates demonstrate typical LBV features in their spectra: broad and strong hydrogen lines, HeI, FeII, and [FeII] lines. All our candidates show photometric variability. We develop a new approach to the LBV parameters estimation based on the inherent property of LBVs to change their spectral type at constant bolometric luminosity. We compare the spectral energy distributions of the variable stars obtained in two or more different states and estimate temperatures, reddening, radii and luminosities of the stars using this method. Two considered candidates (J004526.62+415006.3 and J004051.59+403303.0) have to be classified as new LBV stars. Two more candidates are, apparently, B[e]-supergiants. The nature of one more star (J004350.50+414611.4) is not clear. It does not show obvious LBV-like variability and remains an LBV-candidate.

to appear in MNRAS, 10 pages, 4 figures, 3 tables