A non-contact fingertip sealing device with a fin comprises a non-contact fingertip sealing device part matched with a rotor, wherein the non-contact fingertip sealing device part is formed by sequentially connecting a front baffle, a rear baffle, a high-pressure fingertip sheet and a low-pressure fingertip sheet with a fingertip boot structure; the fin that is arranged in a T shaped manner together with a low-pressure side surface of a fingertip beam and the fingertip boot structure is arranged on the low-pressure fingertip sheet; the fin and a low-pressure fingertip boot utilize hydrodynamic pressure and hydrostatic pressure effects; a lifting force is generated by the action of a front and rear pressure difference and rotation of the rotor to lift the fingertip sheets off the surface of the rotor, so as to achieve sealing and no contact with the rotor; when the rotor has radial displacement, the structure can more effectively and automatically adjust gestures of the fingertip sheets; the motion of the fingertip sheets adapts to radial runout of the rotor; a sealing effect is ensured and a non-contact state is kept at the same time; an effect of reducing and even eliminating the conventional non-contact fingertip sealing 'lag effect' is exerted; and the dynamic sealability of non-contact fingertip sealing is improved.