Electrical resistivity and magnetic susceptibility measurements of the itinerant ferromagnet CoS2 at high pressures reveal that its magnetic ordering temperature is tuned to zero at a critical pressure 4.8 GPa, indicating the existence of a quantum-phase transition. The ambient pressure continuous magnetic-phase transition in CoS2 becomes first order on a very slight pressure increase, with a tricritical point probably located almost at ambient pressure. No deviations from Fermi-liquid behavior were found in the vicinity of the quantum-phase transition in CoS2, implying its strong first-order nature.