Given a skew-symmetric matrix X, the Pfaffian of X is defined as the square root of the determinant of X. In this article, we give the explicit defining equations of Rees algebra of Pfaffian ideal I generated by maximal order Pfaffians of generic skew-symmetric matrices. We further prove that all diagonal subalgebras of the corresponding Rees algebra of I are Koszul. We also look at the Rees algebra of Pfaffian ideals of linear type associated to certain sparse skew-symmetric matrices. In particular, we consider the tridiagonal matrices and identify the corresponding Pfaffian ideal to be of Gröbner linear type and as the vertex cover ideal of an unmixed bipartite graph. As an application of our results, we conclude that all their powers have linear resolutions.