The solid solution of antimonide-oxides Ba1-xKxTi2Sb2O (0 < x < 1) has been synthesized by solid-state reactions and characterized by X-ray powder diffraction (CeCr2Si2C-type structure; P4/mmm, Z = 1). The crystal structure consists of Ti2Sb2O-layers that are stacked with layers of barium atoms along the c-axis. BaTi2Sb2O is a known superconductor with a critical temperature (Tc) of 1.2 K. Substitution of barium through potassium raises Tc up to 6.1 K at 12 % potassium, while no superconductivity emerges with concentrations higher than 20 %. Anomalies in electrical transport and magnetic susceptibility indicate charge density wave (CDW) instabilities. The CDW transition temperatures (Ta) decrease from 50 K in the parent compound to 28 K at 10 % potassium substitution. No CDW transition was detected at higher concentrations, and no evidence for a reduction of the lattice symmetry below Ta was found. The lattice parameters vary linearly while the unit cell volume increases with higher potassium concentrations. The phase diagrams Tc(x) and Ta(x) of Ba1-xKxTi2Sb2O are remarkably similar to the known series Ba1-xNaxTi2Sb2O (0 < x < 0.33) in spite of the reverse volume effect. From this we conclude that the charge and not the volume determines the phase diagrams of these superconducting antimony oxides.