The molecular cloud, embedding AFGL 2591, has a "head-and-tail" structure with a total mass of ${\sim}\;1800\;M_{\odot}$, about half of the mass (${\sim}\;900\;M_{\odot}$) in the head (size ${\sim}\;1.2\;pc$ in diameter), and another half in the envelope (${\sim}\;3.5\;pc$ in the east-west direction). We found a new cloud in the direction toward north-east from AFGL 2591 (projected distance ${\sim}\;2.4\;pc$), which is probably associated with the AFGL 2591 cloud. The $^{12}CO$ spectrum clearly shows a blue-shifted high-velocity wing at around the velocity $-20\;{\sim}\;-10\;km\;s^{-1}$, but it is not clear whether this high-velocity component has a bipolar nature in our observations. The observed CN spectra also show blue-shifted wing component but the existence of the red-shifted component is not clear, either. In some CN and HCN spectra, the highvelocity components appear as a different velocity component, not a broad line-wing component. The dense cores, traced by CN and HCN, exist in the 'head' of the AFGL 2591 cloud with an elongated morphology roughly in the north-south direction with a size of about 0.5 pc. The abundance ratio between CN and HCN is found to be about 2 - 3 within the observed region, which may suggest a possibility that this core is being affected by the embedded YSOs or by possible shocks from outside.