Received 29 December 2009; revised manuscript received 16 February 2010; published 30 March 2010 We have investigated the effect of pressure on the magnetic and structural properties of the frustrated heavy-fermion antiferromagnet YbAgGe in an extended pressure range up to 20 GPa using electrical resistivity and x-ray diffraction, respectively. We find that with increasing pressure, the magnetic ordering temperature Tm first increases rapidly, passes through a maximum Tm=5.4 K at 6.8 GPa, and then drops toward zero for p above 16 GPa, while the structure remains unchanged up to about 20 GPa. We attribute the anomalous pressure dependence of Tm to a complex interplay between the Kondo effect, Ruderman-Kittel-Kasuya-Yosida interactions and the geometrical frustration of the magnetic interactions of the Yb moments in the Kagomelatticelike structure of YbAgGe. We further discuss the competition between geometrical frustration and longrange magnetic order together with the possible occurrence of a pressure-induced second quantum critical point in YbAgGe.