In this paper we improve the electrical characteristics of a short channel silicon on insulator metal-oxide-semiconductor-filed-effecttransistor (SOI-MOSFET), with a graphene sheet incorporated on top of the channel (under oxide) close to the source side and a proportionally p-type retrograde doping region which is embedded almost in the middle of the channel. Because graphene sheet and retrogradedoping are simultaneously utilized in the channel, this structure is called "GR-SOI" transistor. Retrograde dopingcauses impurity scattering in the depth of the channel and it virtually decreases the silicon channel thickness. Since graphene sheet has a small bandgap and high mobility, we use it to virtually reduce the channel length, and enhance the ON-current. An immense comparison among our proposed structure (GR-SOI), a structure similar to GR-SOIbut without graphene (R-SOI), and a conventional structure (C-SOI), shows that our proposed device presentssuperior electrical characteristics and reliability compared with its counterparts. Moreover, we investigate the optimum place for locating the graphene sheet along the channel. The obtained results for the drive current, leakage current, subthreshold swing and maximum transconductance are 7.6 mA, 10 pA, 86 mV/dec and 18.5 mS, respectively. Our simulations indicate GR-SOI transistor can be a serious candidate for digital and analog applications.