GK Cep is an eclipsing binary that contains two A-type components with an orbital period of 0.936d. The high mass ratio and the contact or near-contact configuration make it a key target to understand binary evolution. However, the physical properties and evolutionary state are still unknown. Here we present the UV light curve obtained by using the lunar-based ultraviolet telescope (LUT) and several eclipse times obtained with the Sino-Thai 70-cm telescope and the 1.0-m telescope at Yunnan Observatories. Analysis of the LUT light curve suggests that GK Cep is a near-contact semidetached system where the slightly less massive component is the hotter one that is filling the critical Roche lobe. Meanwhile, a hotspot is found on the neck of the more massive but cooler component. By using all available times for the light minimum, it is detected that the O-C curve shows a cyclic oscillation while it undergoes an upward parabolic change. The increase of the orbital period, the high mass ratio, the semidetached configuration with a lobe-filling less massive component, and the presence of a hotspot on the more massive component all suggest that GK Cep is in a key evolutionary state just after the shortest-period evolutionary stage during the rapid mass transfer. The cyclic change in the O-C curve reveals that GK Cep contains a solar-type stellar companion in a triply hierarchical system that is in agreement with the spectroscopic result. The third body contributes about 2.6 per cent to the total light of the triple system.