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Stellar rotation plays a key role in the transfer of angular momentum, and a large sample of Be-type stars with reliable projected rotational velocities is crucial for understanding their formation and evolution. In this work, we derive the projected rotational velocities ($v$\,sin\,$i$) of 479 Be-type stars using the Fourier transform method, based on their LAMOST Medium-resolution Survey (MRS) spectra. Our results suggest that the Fourier transform method can provide reliable $v$\,sin\,$i$ values for Be-type stars by analyzing the \ion{He}{1}\,lines at 4922, 5015, 5047, and 6678 \,Åin their LAMOST MRS spectra. A K-S test indicates that Be-type stars with different H$α$ emission line morphologies exhibit different $v$\,sin\,$i$ distributions, and Be-type stars with double-peaked emission have a higher fraction of rapid rotators than those with single-peak emission. The $v$\,sin\,$i$ distributions of our Be-type stars in the field, OB associations, and clusters show no significant differences. The deconvolved $v$\,sin\,$i$ distribution of our entire Be-type star sample does not exhibit a bimodal distribution but rather a single peak at $v\approx260$\,km$\cdot$s$^{-1}$. Based on the analysis of 105 stars in our sample, we find that the mean equatorial rotational velocity is 0.74 times the critical velocity. Furthermore, we investigate the relationship between $v$\,sin\,$i$ and the H$α$ peak separation velocity for Be-type stars exhibiting double-peak H$α$ emission lines, using Pearson and Spearman rank correlation coefficients.