New multiband CCD photometry is presented for the eclipsing binary GW Gem; the RI light curves are the first ever compiled. Four new minimum timings have been determined. Our analysis of eclipse timings observed during the past 79 years indicates a continuous period increase at a fractional rate of +(1.2+/-0.1)x10^10^, in excellent agreement with the value +1.1x10^-10^ calculated from the Wilson-Devinney binary code. The new light curves display an inverse O'Connell effect increasing toward longer wavelengths. Hot- and cool-spot models are developed to describe these variations but we prefer a cool spot on the secondary star. Our light-curve synthesis reveals that GW Gem is in a semidetached, but near-contact, configuration. It appears to consist of a near-main-sequence primary star with a spectral type of about A7 and an evolved early K-type secondary star that completely fills its inner Roche lobe. Mass transfer from the secondary to the primary component is responsible for the observed secular period change.