We investigate the possible pair of charmed spin 1/2 and spin 3/2 baryons, or one charmed baryon and one charmed antibaryon within the variational scheme. The Yukawa-like and one-boson-exchange (OBE) potentials are incorporated and we obtain the binding energy and mass spectrum of $\Xi_c$ di-baryon for different spin states. Our results show the possible molecular state with a quantum number $(I, J^P)$=$(1, 0^+), (0,1^+), (1,0^+), and (0,3^+)$. The obtain results of $\Xi_{c}$ $\Xi_{c}$ and
$\Xi_c^{*}$ $\Xi_c^{*}$ di-baryons are in accordance with other theoretical predictions.}