The invention relates to a vehicle dashboard crossmember (2) including a crossbar which extends lengthwise along a generatrix line (G) that is directed substantially along the width of the vehicle body and transversely relative to the direction of travel of said vehicle, as well as at least one connection flange (3, 4) designed to enable said crossbar (2) to be attached to said body, said crossbar (2) consisting, over at least a portion of the length thereof, of a load-bearing web (10) that has a side wall (11) rounded about said generatrix line (G) so as to have, in a cross-section perpendicular to the generatrix line, a first arm (12) and a second arm (13) that are connected to one another via a common connection portion (14) and which thus define a cavity (15), and of a reinforcing brace (20) made of a fibrous composite material.