The mean stellar alpha-to-iron abundance ratio ([$alpha$/Fe]) of a galaxy is an indicator of galactic star formation timescale. It is important for understanding the star formation history of early-type galaxies (ETGs) as their star formation processes have basically stopped. Using the model templates which are made by Vazdekis et al., we apply the pPXF based spectral fitting method to estimate the [$alpha$/Fe] of 196 high signal-to-noise ratio ETGs from the MaNGA survey. The velocity dispersions within 1R$_e$ ($sigma_{e}$) range from 27 to 270 km/s. We find a flat relation between the mean [$alpha$/Fe] within the 1R$_e^{maj}$ ellipses and log($sigma_{e}$), even if limiting to the massive sample with log($sigma_{e}$/km s$^{-1}$)$>$1.9. However, the relation becomes positive after we exclude the Mg$_1$ feature in our fits, which agrees with the results from the previous work with other stellar population models, albeit with relatively large scatter. It indicates that the spectral fits with Vazdekis models could give basically the consistent predictions of [$alpha$/Fe] with previous studies when the Mg$_b$ index is used, but do not work well at the Mg$_1$ band when their $alpha$-enhanced version is employed in the metal-rich regime. We suggest avoiding this rather wide index, which covers 471AA, as it might suffer from other effects such as flux-calibration issues. For reference, we also measure the stellar population radial gradients within 1R$_e^{maj}$ ellipses. Due to the low resolution of age estimations for old objects and the Mg$_1$ issue, the uncertainties of these gradients cannot be neglected.