The upper bound \[ ıt_2^T|G(\hf+\I t)|^2ṭ l Tog^2T \] is proved, where initially $G(s) = \sum\limits_{\g>0}\g^{-s}$. Here $\g$ denotes ordinates of complex zeros of the Riemann zeta-function $\z(s)$. This coincides with the lower bound for the integral in question.