We report the transport and thermodynamic properties under hydrostatic pressure in the antiferromagnetic Kondo compound CeMg2CU9 with a two-dimensional arrangement of Ce atoms. Magnetic specific heat C-mag(T) shows a Schottky-type anomaly around 30 K originating from the crystal electric field (CEF) splitting of the 4f state with the first excited level at Delta(1/)k(B) = 58 K and the second excited level at A(2)/k(B) = 136 K from the ground state. Electric resistivity shows a two-peak structure due to the Kondo effect on each CEF level around T-1(max) = 3 K and T-2(max) = 40 K. These peaks merge around 1.9GPa with compression. With increasing pressure, Nee] temperature T-N initially increases and then changes to decrease. TN finally disappears at a quantum critical point P-c = 2.4GPa.