A reflexive polytopes play an important role in many mathematical directions such as algebraic, combinatorics, and mathematical geometry, in addition to its importance in mathematics directions, some physical applications need reflexive polytope to work on it. Therefore we shall take this kind of polytopes in mind. A rich source of open problems and conjectures are made by a reflexive polytopes, which is a mirror symmetry conjectures in theoretical physics, besides their various questions in toric of geometry, the error-correcting codes and random walks. In this work, the reflexive polytope with some definitions and theorems about it are studied. The Ehrhart polynomial of a polytope is also discussed with some theorems and examples. The relation between the h-vectors of the Ehrhart series with the number of integer points is discussed. New relation between the h-vector and the number of integer points is given. For simplicial reflexive polytope the proof of the maximal number of vertices is also introduced.