Observed spectra of quasars provide a powerful tool to test the possible spatial and temporal variations of the fine-structure constant α = e2/ћc over the history of the Universe. It is demonstrated that high sensitivity to the variation of α can be obtained from a comparison of the spectra of quasars and laboratories. We reported a new constraint on the variation of the fine-structure constant based on the analysis of the optical spectra of the fine-structure transitions in [NeIII], [NeV], [OIII], [OI] and [SII] multiplets from 14 Seyfert 1.5 galaxies. The weighted mean value of the α-variation derived from our analysis over the redshift range 0.035 < z < 0.281 Δα/α= (4.50 ± 5.53) \times 10-5. This result presents strong limit improvements on the constraint on Δα/α compared to the published in the literature