The invention relates to the use of an organic-inorganic hybrid material, comprising an inorganic solid support on which are grafted organic molecules having the general formula (I) below: in which: x, y and z=0 or 1, with at least one of x, y and z different from 0; m=1 to 6; v and w=0 or 1, with v=1 when w=0, and v=0 when w=1; if x=0, R1═H or a saturated or unsaturated, linear or branched, C1 to C12 hydrocarbon group, whereas, if x=1, R1=a group bound to the inorganic solid support by at least one covalent bond; if y=0, R2═H or a saturated or unsaturated, linear or branched, C1 to C12 hydrocarbon group, whereas, if y=1, R2=a group bound to the inorganic solid support by at least one covalent bond; if z=0, R3═H or a saturated or unsaturated, linear or branched, C1 to C12 hydrocarbon group, whereas, if z=1, R3=a group bound to the inorganic solid support by at least one covalent bond; R4 and R5═H, a saturated or unsaturated, linear or branched, C2 to C8 hydrocarbon group, or a monocyclic aromatic group; for extracting uranium(VI) from a sulfuric acid aqueous solution. The invention also relates to a method that makes it possible to recover the uranium(VI) present in a sulfuric acid aqueous solution, selectively with respect to the other metal cations that may also be present in said solution.