We investigate the possible pair of charmed spin 1/2 and spin 3/2 baryons within the variational scheme. Incorporating the Yukawa-like and one-boson-exchange, we obtain the binding energy and mass spectrum of $\Xi_c$ dibaryon 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 obtained results of $\Xi_{c}$-$\Xi_{c}$ and
$\Xi_c^{*}$ -$\Xi_c^{*}$ dibaryons are in accordance with theoretical predictions.