A radiation-reaction trapping (RRT) of electrons is revealed in the near-QED regime of laser-plasma interaction. Electrons quivering in laser pulse experience radiation reaction (RR) recoil force by radiating photons. When the laser field reaches the threshold, the RR force becomes significant enough to compensate for the expelling laser ponderomotive force. Then electrons are trapped inside the laser pulse instead of being scattered off transversely and form a dense plasma bunch. The mechanism is demonstrated both by full three-dimensional particle-in-cell simulations using the QED photonic approach and numerical test-particle modeling based on the classical Landau-Lifshitz formula of RR force. Furthermore, the proposed analysis shows that the threshold of laser field amplitude for RRT is approximately the cubic root of laser wavelength over classical electron radius. Because of the pinching effect of the trapped electron bunch, the required laser intensity for RRT can be further reduced.
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