In this paper, we considered the cosmological application by taking G and Λ to be a function of t in Kaluza-Klein cosmology. We use the Taylor’s expansion of cosmological function Λ(t), up to the first order of time t and evaluated the cosmological parameters by using the modified equation of state of the form p = −ρ − f (ρ), where f (ρ) = αρ. The analytical properties of R(t), ρ(t) and H(t) are investigated and it is observed that from the solutions of the field equations, the generalized sudden singularity occurs at a finite time in the framework of Kaluza-Klein theory of gravitation.