A disc brake for a commercial vehicle has a caliper that straddles a brake disc. The caliper is mounted on a brake carrier on the vehicle side by way of two connecting bearings in an axially displaceable manner in relation to the brake disc. The connecting bearings each include a guide bar that is securely connected to the brake carrier and guided in a slide bearing of the caliper for the axial displacement thereof. At least one connecting bearing is provided with a radially elastic damping bushing, which at least surrounds the guide bar in regions and has grooves that are laterally delimited by ribs. The disc brake is designed such that the damping bushing has a progressive damping behavior in the radial loading direction.