In this paper I address the debate between Newton and Leibniz on the concept of Time. The biggest difference between their distinct conceptions of time is that whether time is absolute or relative; Newton holds that real time is absolute, which is independent of the existence of things; on the contrary, Leibniz holds that time is relational to the things, which implies that there is no time, were there no things. In this debate, Leibniz provided his argument against Newton in the letters to Clarke. So my research is mainly based on the correspondence between Leibniz and Clarke. I hope to clarify the true standpoint of both and furthermore to judge whether Leibniz's criticism is right. And if Leibniz is right, is it possible to modify Newton's conception of time, but otherwise also to maintain the essence of his conception? And finally, I hope also to inspect Leibniz's conception, to see whether it is confronted with different difficulties. Therefore this paper contains four parts: First, the Newtonian conception of absolute time. Second, Leibniz's criticism and the conception of relative time. Third, principle of sufficient reason and principle of identity. Finally, the difficulty of the relative conception of time. In the first two parts, I analyze Newton's and Leibniz's conceptions of time respectively and also Leibniz's criticism. In the third part, I attempt to modify the Newtonian conception to avoid Leibniz's criticism. In the final part, I attempt to point out the difficulty of the Leibnizian conception.