Let f be a newform for the group |$\Gamma_{0}(q)$| and χ d be a primitive quadratic character of conductor |$|d|$|. In this article, we prove an asymptotic for the second moment of the derivative of |$L(s,\, f \otimes \chi_{8d})$| at the central point |$1/2$| , which was previously known under grand Riemann hypothesis (GRH) by Petrow [ 9 ].