Molecular dynamics simulations have been performed to characterise the stability behaviour of graphene nanoribbons having different hydrogen coverage, subject to a uniaxial compressive load. The temperature is set at a very low value to circumvent the contribution of thermal agitations. The results show that hydrogen coverage promotes to a rapid drop in the strain of buckling onset due to the effects of easy rotation of newly unsupported sp3 bonds. Furthermore, we have also found a critical value of the hydrogen adsorption above which the declining trend in the stability behaviour of hydrogenated graphene nanoribbons is reversed.