In this article, we attempted a study on field effect transport characteristics of graphene flakes. These graphene flakes were exfoliated by mechanical peeling-off technique and the electrical contacts were patterned by photo-lithographic method. Graphene devices have shown better transfer characteristics which was obtained even in low-voltage (< 5 V). Back-gated graphene transistors were patterned on oxidized silicon wafers. A clear n-type to p-type transition at Dirac point and higher electron drain-current modulation in positive back-gate field with current minimum (the Dirac point) were observed at V(GS) = -1.7 V. The carrier mobility was determined from the measured transconductance. The transconductance of the graphene transistors was observed as high as 18.6 microS with a channel length of 68 microm. A maximum electron mobility of 1870 +/- 143 cm2/V x s and hole mobility of 1050 +/- 35 cm2/V x s were achieved at a drain bias 2.1 V which are comparatively higher values among reported for mechanically exfoliated graphene using lithographic method. The fabricated devices also sustained with high-current density for 40 hr in continuous operation without any change in device resistance, which could be applied for robust wiring applications.