A theoretical study of rotational collision of LiH(X1Σ+,v = 0, J) with Ar has been carried out. The ab initio potential energy surface (PES) describing the interaction between the Ar atom and the rotating LiH molecule has been calculated very accurately and already discussed in our previous work [Computational and Theoretical Chemistry 993 (2012) 20–25]. This PES is employed to evaluate the de-excitation cross sections. The ab initio PES for the LiH(X1Σ+)-Ar(1S) Van der waals system is calculated at the coupled-cluster [CCSD(T)] approximation for a LiH length fixed to an experimental value of 3.0139 bohrs. The basis set superposition error (BSSE) is corrected and the bond functions are placed at mid-distance between the center of mass of LiH and the Ar atom. The cross sections are then derived in the close coupling (CC) approach and rate coefficients are inferred by averaging these cross sections over a Maxwell-Boltzmann distribution of kinetic energies. The 11 first rotational levels of rate coefficients are evaluated for temperatures ranging from 10 to 300 K. We notice that the de-excitation rate coefficients appear large in the order 10−10 cm−3 s−1 and show very low temperature dependence. The rate coefficients magnify significantly the propensity toward ∆ J = −1 transitions. These results confirm the same propensity already noted for the cross sections.