In this work, we investigate the prompt $J/psi$ production in associated with top quark pair to leading order in the nonrelativistic QCD factorization formalism at the LHC with $sqrt{s} =13$ TeV. In addition to the contribution from direct $J/psi$ production, we also include the indirect contribution from the directly produced heavier charmmonia $chi_{cJ}$ and $psi^prime$. We present the numerical results for the total and differential cross sections and find that the $sideset{^3}{^{(8)}_1}{mathop{{S}}}$ states give the dominant contributions. The prompt $tbar t J/psi$ signatures at the LHC are analyzed in the tetralepton channel $ppto (tto W^+(ell^+ u)b) (bar t to W^-(ell^- bar u)bar b) (J/psitomu^+mu^-)$ and trilepton channel $ppto (tto W(q q^prime)b) ( t to W(ell u) b) (J/psitomu^+mu^-)$, with the $J/psi$ mesons decaying into muon pair, and the top quarks decaying leptonically or hadronically. We find that $tbar t J/psi$ proudction can be potentially detected at the LHC, whose measurement is useful to test the heavy quarkonium production mechanism.
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