In this paper I will discuss the notion of infinity (that is, the notion of infinite causal series) and the principle of sufficient reason, to determine the plausibility of cosmological argument. The problem of infinity started with Philoponus’ critique of Aristotle’s theses of the eternity of the world and impossibility of actual infinity. In a section about historical context I will present few interesting arguments. After I discuss some crucial points of these arguments, I will try to defend the principle of sufficient reason from classical objections, and then answer the question ‘Does the cosmological argument fulfill the requirements of the principle of sufficient reason?’. I think that we are witnessing the growth of cosmological argument due to theoretical and scientific improvements, and significant cosmological researches of today.