The device (1) comprises a first means (3) for measuring the effective value of the velocity vector of the aircraft, a computing unit (4) which determines a display value automatically and repetitively and which comprises a filtering means (6) which filters the value measured by the first means (3) so as to form a first term, a display unit (7) for presenting on a screen (2) a characteristic sign illustrating the velocity vector whose position on the screen (2) is representative of the display value, and a second means (9) for determining the derivative of a velocity vector controlled by an aircraft pilot. The computing unit (4) further comprises a computing means (10) which determines a second term from the derivative of the controlled velocity vector and a summator (12) which sums the first and second terms so as to form the display value.