Thorough resistivity measurements on single crystals of CeZn11 under pressure p and magnetic field H are presented. At ambient pressure, CeZn11 orders antiferromagnetically at TN=2 K. The pressure dependence of the resistivity reveals an increase of the Kondo effect. We determine the pressure evolution of the magnetic exchange interaction between conduction and localized 4f electrons. It qualitatively reproduces the pressure evolution of the magnetic ordering temperature TO1 (with TO1=TN at ambient pressure). In addition to TO1, a new anomaly TO2appears under pressure. Both anomalies are found to increase with applied pressure up to 4.9 GPa, indicating that CeZn11 is far from a pressure induced quantum critical point. Complex T-H phase diagrams are obtained under pressure which reveal the instability of the ground state in this compound.