Abstract: I will discuss string one-loop contributions to Einstein-Hilbert term in toroidal minimally supersymmetric type IIB orientifolds with D-branes. This study is indispensable in order to determine the quantum corrections to Kahler metric of the moduli scalars in these models. I will describe the procedures of the calculations of the string-loop Einstein Hilbert term for a general compact type IIB $Z_N$ orientifolds, which is a missing gap in literature, and illustrate the results in two concrete examples, i.e. $Z_3$ and $Z_6$ models.