We theoretically propose possible magnetism-induced negative thermal expansion in honeycomb-lattice antiferromagnets with edge-sharing networks of $MX_6$ octahedra where $M$ and $X$ are transition-metal and ligand ions, respectively. In this crystal structure, the nearest-neighbor exchange interaction is composed of two competing contributions, i.e., the antiferromagnetic contribution from a direct 180$^circ$ $M$-$M$ bond and the ferromagnetic contribution from 90$^circ$ $M$-$X$-$M$ bonds, amplitudes of which have different bond-length dependence. Numerical analysis of the spin-lattice model of the honeycomb-lattice antiferromagnets demonstrates that the negative thermal expansion can occur when the system enters the antiferromagnetic phase with lowering temperature so as to maximize the energy gain associated with the bond-length dependent antiferromagnetic exchange interaction. The present work provides a guiding principle for searching new materials and eventually contributes to diversify the family of materials that host the negative thermal expansion originating from the spin-lattice coupling on the honeycomb lattices or related crystal structures.
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