We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant ( ) and cosmological constant ( ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent and . A variety of solutions have been found in which increases and decreases with time , which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail. 1. Introduction The observational analysis of High-Redshift Type Ia Supernova and Supernova Cosmological Project [1–5] provided a wealth of information about our universe. These observational analyses imply that a positive cosmological constant of order ( ) may dominate the total energy density in the universe and that the expansion of the universe is accelerating [6]. Higher-dimensional cosmological models play a vital role in many aspects of early stage of cosmological problems, one of the frontier areas of research to unify gravity with other forces in nature. The study of higher-dimensional space-time provides an idea that our universe was much smaller at early stage of evolution than observed today. The detection of extra dimensions in current experiments is beyond those four dimensions observed so far. Over the past few years, a lot of attention was received on cosmological models in which space-time has more than five dimensions. The field of cosmology has been highly enriched by the Kaluza-Klein theory [7, 8], in which they have shown that gravitation and electromagnetism could be unified in a single geometrical structure. Chodos and Detweiler obtained a higher-dimensional cosmological model in which an extra dimension contracts and indicates that this contraction of extra dimension is a consequence of cosmological evolution [9]. Guth and Alvarez and Gavela noticed that during contraction process extra dimensions produce massive amount of entropy, which provides an alternative resolution to the flatness and horizon problems as compared to the usual inflationary scenario [10, 11]. A number of authors [12–22] obtained the solutions of Einstein’s field equations for higher-dimensional space-times containing a variety of matter fields. In their analysis, some authors have shown that there is an expansion of the four-dimensional space-times while the fifth dimension contracts or remains constant. The concept of a variable gravitational constant was first proposed by Dirac in 1937 [23]. In 1985, Lau proposed modifications linking the variation of
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