This article presents a systematic investigation of various integral and computational representations for family of General Hurwitz – Lerch Zeta function . In this paper new results for Generalized Hurwitz – Lerch Zeta function are established.Certain known integral representation for generalized Riemann Zeta function is obtained as special cases of main results. In this paper we established five results, these results presents the different forms of integral representations of generalized Hurwitz-Lerch Zeta function.