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We report a search for a dark photon using $14.9$~fb$^{-1}$ of $e^+e^-$annihilation data taken at center-of-mass energies from 4.13 to 4.60~GeV withthe BESIII detector operated at the BEPCII storage ring. The dark photon isassumed to be produced in the radiative annihilation process of $e^+e^-$ and topredominantly decay into light dark matter particles, which escape from thedetector undetected. The mass range from 1.5 to 2.9~GeV is scanned for the darkphoton candidate, and no significant signal is observed. The mass dependentupper limits at the 90$\%$ confidence level on the coupling strength parameter$\epsilon$ for a dark photon coupling with an ordinary photon vary between$1.6\times 10^{-3}$ and $5.7\times10^{-3}$.

Search for invisible decays of a dark photon using $e^+e^-$ annihilation data at BESIII