Selective adsorptive capture and separation of chemically inert krypton (Kr) and xenon (Xe) noble gases with very low ppmv concentrations in air and industrial off-gases constitute an important technological challenge. Here, using a synergistic combination of experiment and theory, the microporous crystalline vanadomolybdates (MoVOx) as highly selective Kr sorbents are studied in detail. By varying the Mo/V ratios, we show for the first time that their one-dimensional (1D) pores can be fine-tuned for the size-selective adsorption of Kr over the larger Xe with selectivities reaching >100. Using extensive electronic structure calculations and grand canonical Monte Carlo simulations, the competition between Kr uptake with CO2 and N2 was also investigated. As most materials reported so far are selective toward the larger, more polarizable Xe than Kr, this work constitutes an important step toward robust Kr-selective sorbent materials. This work highlights the potential use of porous crystalline transition metal oxides as energy-efficient and selective noble gas capture sorbents for industrial applications.