A lumbar support for a vehicle backrest has a rest member with a front surface shaped to support an area of a user's back, and an elastic member behind the rest member; the elastic member has an intermediate portion fixed to the rest member and two opposite ends fixed connected to a backrest frame, maintains the rest member in a rest position and can deform in response to a thrust of the user's back so as to let the rest member move between the rest position and a first position under normal conditions, and then abruptly towards a second position when a thrust of a user's back exceeds a given force value; the force/displacement curve of the elastic member has a slope which is between zero and a given threshold in the section between the first and the second positions, the threshold being equal to 0.5 [N/mm].