Graphene, as a novel category of carbon nanomaterials, has attracted a great attention in the field of drug delivery. Due to its large dual surface area, graphene can efficiently load drug molecules with high capacity via non-covalent interaction without chemical modification of the drugs. Hence, it ignites prevalent interests in developing a new graphene/graphene oxide (GO)-based drug delivery system (GDDS). However, current design of GDDS primarily depends on the prior experimental experience with the trial-and-error method. Thus, it is more appealing to theoretically predict possible GDDS candidates before experiments. Toward this end, we propose to fuse quantum genetic algorithm (QGA) and quantum mechanics (QM)/semi-empirical quantum mechanics (SQM)/force field (FF) to globally search the optimal binding interaction between the graphene/GO and drug in a given GDDS and develop a free computational platform “e-Graphene” to automatically predict/screen potential GDDS candidates. To make this platform more pragmatic for the rapid yet relatively accurate prediction, we further propose a cascade protocol via firstly conducting a fast QGA/FF calculation with fine QGA parameters and automatically passing the best chromosomes from QGA/FF to initialize a higher level QGA/SQM or QGA/QM calculation with coarse QGA parameters (e.g., small populations and short evolution generations). By harnessing this platform and protocol, systematic tests on a typical GDDS containing an anticancer drug SN38 illustrate that high fabrication rates of hydroxyl, epoxy, and carboxyl groups on a pristine graphene model will compromise the stability of GDDS, implying that an appropriate functionalization rate is crucial for the delicate balance between the stability and solubility/biocompatibility of GDDS. Moreover, automatic GDDS screen in the DrugBank database is performed and elicits four potential GDDS candidates with enhanced stability than the commonly tested GDDS containing SN38 from the computational point of view. We hope that this work can provide a useful program and protocol for experimental scientists to rationally design/screen promising GDDS candidates prior to experimental tests.