We have grown crystals Na0.4Y0.6F2.2:Ho3+ (NYF:Ho3+) by the Bridgman-Stockbarger method. The optical spectra and luminescence kinetics of NYF:Ho3+ crystals have been studied. Based on the analysis of low-temperature absorption spectra, we determine the structure of the Stark splitting of holmium levels in NYF:Ho3+ crystals. From absorption spectra examined at T = 300 K, we calculate absorption cross-section spectra and oscillator strengths of transitions from the ground state of holmium to excited multiplets. We show that the absorption spectra of NYF:Ho3+ crystals consist of broad bands that lie in the UV, visible, and near-IR ranges. The most intense bands are observed in the visible range, they correspond to transitions 5I8 → (5F1, 5G6) and 5I8 → (5F4, 5S2), and their maximal absorption cross sections are σabsmax (λ = 450.3 nm) = 1.16 × 10−20 cm2 and σabsmax (λ = 535.1 nm) = 0.9 × 10−20 cm2. The intensity parameters Ωt have been calculated by the Judd-Ofelt method taking into account 10, 12, and 20 transitions from the 5I8 ground state to excited multiplets. We show that, with an increasing number of transitions taken into account in the calculation, the parameters Ωt somewhat increase. For 20 transitions, we have obtained the following intensity parameters: Ω2 = 0.97 × 10−20, Ω4 = 1.74 × 10−20, and Ω6 = 1.15 × 10−20 cm2. With these parameters, we have calculated the probabilities of radiative transitions, the radiative lifetimes, and the branching ratios. The rates of multiphoton nonradiative transitions have been estimated. The luminescence decay kinetics from excited holmium levels 5F3 (5F4, 5S2) and 5F5 have been studied upon selective excitation in the range of 490 nm, and the lifetimes of these levels have been experimentally determined. We find that the calculated and experimental rates of radiative and nonradiative relaxation from excited holmium levels agree well with each other. We show that, upon pumping in the range of 490 nm, the multiplet (5F4, 5S2) is populated as a result of the radiative and nonradiative excitation relaxation from the 5F3 level, while the lower-lying 5F5 level is populated due to direct radiative transitions 5F3, 2 → 5F5, obviating the cascade scheme 5F3 → (5F4, 5S2) ↝ 5F5. We conclude that NYF:Ho3+ crystals are processable; admit doping by holmium in high concentrations (up to 100%); and, with respect to all their radiative characteristics, can be considered as potential active media for solid-state continuously tunable lasers in the IR and visible ranges.