The zonal wave number 1 planetary wave of period near 6.5 days is a robust feature in the mesosphere and lower thermosphere (MLT) region with prominent seasonal variability as revealed by ground based and satellite observations. This wave and its seasonal variability are well reproduced in a recent one model year run of the National Center for Atmospheric Research thermosphere-ionosphere-mesosphere-electrodynamics general circulation model (TIME-GCM) with its lower boundary specified according to the National Centers for Environmental Prediction analysis (year 1993). Wavelet analysis of the model output shows that in the MLT region the wave maximizes before and after the equinoxes and minimizes at solstices. The wave amplitudes at the equinoxes are smaller than the peaks before and after but are still larger than the wave amplitudes at solstices. However, at the lower boundary near 30 km the wave peaks are predominantly between fall and the following spring. By examining the episodes of maximum and minimum wave amplitude and by conducting additional control experiments using the TIME-GCM, the structure of this planetary wave and the factors determining the wave characteristics and seasonal variability are studied in detail. It is found that the wave source, mean wind structure, instability, and the critical layers of the wave can all affect the wave response in the MLT region and can have a strong seasonal dependence. Before and after equinox, the wave follows the waveguide and propagates from the stratosphere to the summer mesosphere/mesopause, where it may amplify due to baroclinic/barotropic instability. Such instability is usually absent from the equinoctial atmosphere, so that there is no wave amplification at equinox. At solstice the wave decays significantly when propagating away from its winter source due to the strong eastward winter stratospheric jet. In the summer side the westward jet is also strong, and the meridional and vertical extension of the critical layer of the wave is large enough to enclose the instability in the summer mesosphere/mesopause at middle to high latitudes. The wave is thus reflected away and prevented from reaching and amplifying at the unstable region. The seasonal variation of the quasi-two-day wave, which has zonal phase speed similar to the 6.5-day wave, is also studied using similar diagnostics. It is further shown that within certain seasonal window periods, the variability in the MLT, especially the summer MLT, may closely track the lower atmospheric variability associated with these waves.