A simple method for exfoliating pristine graphite to yield mono-, bi-, and multi-layers of graphene sheets as a highly concentrated (5.25 mg/mL) and yielded solution in an organic solvent was developed. Pre-thermal treatment of pristine graphite at $900^{circ}C$ in a sealed stainless steel bath under high pressures, followed by sonication in 1-methyl-2-pyrrolidinone solvent at elevated temperatures, produced a homogeneous, well-dispersed, and non-oxidized graphene solution with a low defect density. The electrical conductivities of the graphene sheets were very high, up to 848 S/cm. These graphene sheets were used to fabricate graphene-polyimide nanocomposites, which displayed a higher electrical conductivity (1.37 S/m) with an improved tensile strength (95 MPa). The synthesized graphene sheets and nanocomposites were characterized by transmission electron microscopy, scanning electron microscopy, atomic force microscopy, X-ray photoelectron spectroscopy, and Raman spectroscopy.