A new oxide, sodium-iron antimonate, Na2FeSbO5, was synthesized and structurally characterized, and its static and dynamic magnetic properties were comprehensively studied both experimentally by dc and ac magnetic susceptibility, magnetization, specific heat, electron spin resonance (ESR) and Mossbauer measurements, and theoretically by density functional calculations. The resulting single-crystal structure (a = 15.6991(9) angstrom ; b = 5.3323 (4) angstrom ; c = 10.8875(6) angstrom ; S.G. Pbna) consists of edge-shared SbO6 octahedral chains, which alternate with vertex-linked, magnetically active FeO4 tetrahedral chains. The Fe-57 Mossbauer spectra confirmed the presence of high-spin Fe3+ (3d(5)) ions in a distorted tetrahedral oxygen coordination. The magnetic susceptibility and specific heat data show the absence of a long-range magnetic ordering in Na2FeSbO5 down to 2 K, but ac magnetic susceptibility unambigously demonstrates spin-glass-type behavior with a unique two-step freezing at T-f1 approximate to 80 K and T-f2 approximate to 35 K. Magnetic hyperfine splitting of Fe-57 Mossbauer spectra was observed below T* approximate to 104 K (T-f1 < T*). The spectra just below T* (T-f1 < T < T*) exhibit a relaxation behavior caused by critical spin fluctuations, indicating the existence of short-range correlations. The stochastic model of ionic spin relaxation was used to account for the shape of the Mossbauer spectra below the freezing temperature. A complex slow dynamics is further supported by ESR data revealing two different absorption modes presumably related to ordered and disordered segments of spin chains. The data imply a spin-cluster ground state for Na2FeSbO5.