A graphene channel field-effect biosensor is demonstrated for detecting the binding of double-stranded DNA and poly-l-lysine. Sensors consist of chemical vapor deposition graphene transferred using a clean, etchant-free transfer method. The presence of DNA and poly-l-lysine are detected by the conductance change of the graphene transistor. A readily measured shift in the Dirac voltage (the voltage at which the graphene's resistance peaks) is observed after the graphene channel is exposed to solutions containing DNA or poly-l-lysine. The 'Dirac voltage shift' is attributed to the binding/unbinding of charged molecules on the graphene surface. The polarity of the response changes to positive direction with poly-l-lysine and negative direction with DNA. This response results in detection limits of 8 pM for 48.5 kbp DNA and 11 pM for poly-l-lysine. The biosensors are easy to fabricate, reusable and are promising as sensors of a wide variety of charged biomolecules. © 2015 IOP Publishing Ltd.