To provide a bracket of shock absorber which can be installed to a shock absorber with a sufficient installing strength.

A bracket 8 furnished with a fastening hole 9 where the outer tube 2 of a shock absorber is inserted; a slit 10 opened to the outer periphery by communicating with the fastening hole 9; and tongue pieces 11 formed at both sides of the slit 10; is provided. The bracket 8 gives a fastening force to the shock absorber by adding a clamp pressure to the tongue pieces 11 so as to narrow the width of the slit 10, and it is installed to the shock absorber 1. And the bracket 8 makes at least one side of the pressurizing surfaces where the clamp pressure of the tongue pieces 11 is added, inclined, close to the center line Y of the slit 10, at the closer side to the fastening hole 9, while separating from the center line Y of the slit 10, and the farther side from the fastening hole 9, in the free condition of the tongue pieces 11.