We report on the synthesis and the physical properties of Ba_1−xRb_xTi₂Sb₂O (x≤0.4) by x-ray diffraction, superconducting quantum interference device magnetometry, resistivity, and specific-heat measurements. Upon hole doping by substituting Ba with Rb, we find superconductivity with a maximum T_c=5.4 K. Simultaneously, the charge-density-wave transition temperature is strongly reduced from T_CDW≈55 K in the parent compound BaTi₂Sb₂O and seems to be suppressed for x≥0.2. The bulk character of the superconducting state for the optimally doped sample (x=0.2) is confirmed by the occurrence of a well developed discontinuity in the specific heat at T_c, with ΔC/T_c≈22 mJ/mol K², as well as a large Meissner-shielding fraction of ≈40%. The isotropically averaged lower and upper critical fields of the optimally doped sample (x=0.2) are estimated to μ₀H_c,1(0)≈3.8 mT and μ₀H_c,2(0)≈2.3 T, respectively, indicating that these compounds are strongly type-II superconductors.