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We studied Gr\"uneisen parameter ({\gamma}G) to investigate lattice anharmonicity in a layered BiS2-based superconductor system REO1-xFxBiS2 (RE = La, Ce, Pr, Nd), where in-plane chemical pressure was tuned by substituting the RE elements. With increasing in-plane chemical pressure, bulk modulus remarkably increases, and a high {\gamma}G is observed for RE = Nd. The dependence of {\gamma}G on in-plane chemical pressure exhibits a good correlation with Tc, and a higher Tc is achieved when {\gamma}G is large for RE = Nd. In addition, {\gamma}G shows a slight decrease by a decrease of F concentration (x) in REO1-xFxBiS2. Our results show that the anharmonic vibration of Bi along the c-axis is present in REO1-xFxBiS2, and the enhancement of the anharmonicity is positively linked to superconducting Tc and pairing mechanisms.