To provide support suspension structure for a vehicle capable of precisely fastening a shock absorber having excellent durability without causing increase of the number of parts or man-hour for assembling.

The suspension structure is equipped with a shock absorber 18, a shock absorber bracket 27, and a centering bracket 28. The shock absorber 18 is connected to a cross member 3 through a lower arm 13. The shock absorber bracket 27 is composed of an upward wall part 273 having a mounting hole 42 and a cylinder part 271 which extends downward from the outer peripheral part of the wall part 273 and is fixed to the cross member 3 side. The centering bracket 28 has a turned cup shaped part 281 where a centering hole 43 making a concentric hole with the mounting hole 42 and a driving part 44 which encloses the centering hole 43 and is abuttable to the upward wall part 273 are formed, and the lower end part 282 is firmly fixed to the outer peripheral wall of the cylinder part 271 in a state covered by the upward wall part 273. The bolt shaft 47 of the shock absorber 18 are inserted into the mounting hole 42 and the center ring hole 43 to be fasten.