Let $(H, \beta)$ be a monoidal Hom-Hopf algebra with the bijective antipode $S$, In this paper, we mainly construct the Drinfel'd codouble $T(H)=(H^{ op}\otimes H^{ *}, \beta\otimes \beta^{ *-1})$ and $\widehat{ T(H)}=( H^{ *}\otimes H^{ op}, \beta^{ *-1}\otimes \beta)$ in the setting of monoidal Hom-Hopf algebras. Then we prove both $T(H)$ and $\widehat{ T(H)}$ are coquasitriangular. Finally, we discuss the relation between Drinfel'd codouble and Heisenberg double in the setting of monoidal Hom-Hopf algebras, which is a generalization of the part results in \cite{ L94}.
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