The kagome metal KV3Sb5 hosts charge order, topologically nontrivial Dirac band crossings, and a superconducting ground state with unconventional characteristics. Here we study the evolution of charge order and superconductivity in KV3Sb5 under hydrostatic pressure using electrical resistivity measurements. With the application of pressure, the ambient pressure superconducting transition temperature Tc ≈ 0.9 K increases to ≈ 3.1 K at 0.4 GPa, while the charge ordering temperature T * decreases from 78 K to 50 K. Upon further increasing pressure, charge order disappears in a first-order-like fashion at a pressure p0 just above 0.4 GPa, and Tc undergoes a small reduction from 3.1 K for 0.4 GPa to 2.6 K for 2.25 GPa. Thus, relative to its ambient pressure value of ≈ 0.9 K, Tc is enhanced over a broad pressure range beyond p0. These results suggest that the increase of Tc with the suppression of charge order results from a competition between the two orders. In addition, the upper critical field µ0Hc2(T = 0) is significantly enhanced near the critical pressure p0, but µ0Hc2(T ) at various pressures can be well scaled.