BVR CCD observations of GW Cep were made on 15 nights in November through December 2008 with a 1-m reflector at the Jincheon station of the Chungbuk National University Observatory. Nineteen new times of minimum lights for GW Cep were determined and added to a collection of all other times of minima available to us. These data were then intensively analyzed, by reference to an O-C diagram, to deduce the general form of period variation for GW Cep. It was found that the O-C diagram could be interpreted as presenting two different forms of period change: an exclusively quasi-sinusoidal change with a period of 32.6 years and an eccentricity of 0.10; and a quasi-sinusoidal change with a period of 46.2 years and an eccentricity of 0.36 superposed on an upward parabola. Although a final conclusion is somewhat premature at present, the latter seems more plausible because late-type contact binaries allow an inter-exchange of both energy and mass between the component stars. The quasi-sinusoidal characteristics were interpreted in terms of a light-time effect due to an unseen tertiary component. The minimum masses of the tertiary component for both cases were calculated to be nearly the same as the $0.23-0.26M;{odot}$-ranges which is hardly detectable in a light curve synthesis. The upward parabolic O-C diagram corresponding to a secular period increase of about $4.12{ imes}10^{-8};d/yr$ was interpreted as mass being transferred from the lesser to more massive component. The transfer rate for a conservative case was calculated to be about $2.66;{ imes};10^{-8};M_{odot}/yr$ which is compatible with other W UMa-type contact binaries.