A simple one-stage solution-based method was developed to produce graphene nanoribbons by sonicating graphite powder in organic solutions with polymer surfactant. The graphene nanoribbons were deposited on a silicon substrate, and characterized by Raman spectroscopy and atomic force microscopy. Single-layer and few-layer graphene nanoribbons with a width ranging from sub-10 nm to tens of nanometers and lengths ranging from hundreds of nanometers to 1 µm were routinely observed. The electrical transport properties of individual graphene nanoribbons were measured in both the back-gate and polymer-electrolyte top-gate configurations. The mobility of the graphene nanoribbons was found to be over an order of magnitude higher when measured in the latter than in the former configuration (without the polymer-electrolyte), which can be attributed to the screening of the charged impurities by the counter ions in the polymer-electrolyte. This finding suggests that the charge transport in these solution produced graphene nanoribbons is largely limited by charge impurity scattering.