The [{alpha}/Fe] ratios in stars are good tracers to probe the formation history of stellar populations and the chemical evolution of the Galaxy. The spectroscopic survey of LAMOST provides a good opportunity to determine [{alpha}/Fe] of millions of stars in the Galaxy. We present a method of measuring the [{alpha}/Fe] ratios from LAMOST spectra using the template-matching technique of the LSP3 pipeline. We use three test samples of stars selected from the ELODIE and MILES libraries, as well as the LEGUE survey to validate our method. Based on the test results, we conclude that our method is valid for measuring [{alpha}/Fe] from low-resolution spectra acquired by the LAMOST survey. Within the range of the stellar parameters Teff=[5000, 7500]K, logg=[1.0, 5.0]dex and [Fe/H]=[-1.5, +0.5]dex, our [{alpha}/Fe] measurements are consistent with values derived from high-resolution spectra, and the accuracy of our [{alpha}/Fe] measurements from LAMOST spectra is better than 0.1dex with spectral signal-to-noise higher than 20.