The invention relates to an elevator brake, said elevator comprising a hoisting machine (1) provided with at least a frame part (2) and a traction sheave (3), and a brake drum (4) arranged to be rotatable with the traction sheave (3) and provided with a braking surface (5), and a brake (6) having an effect on the rotary motion of the traction sheave (3), said brake (6) comprising at least one brake block (8) provided with a braking surface, which brake block (8) has been arranged to act on the braking surface (5) of the brake drum (4) with a force directed substantially towards the braking surface (5). To allow adjustment of the size of the air gap (8a) between the braking surface of the brake block (8) and the braking surface (5) of the brake drum (4), the brake (6) is provided with at least one eccentric adjusting element (11).