In this work we test graphene electrodes in nano-metric channel n-type Organic Field EffectTransistors (OFETs) based on thermally evaporated thin films of perylene-3,4,9,10-tetracarboxylic acid diimide derivative (PDIF-CN2). By a thorough comparison with short channel transistors made with reference gold electrodes, we found that the output characteristics of the graphene-based devices respond linearly to the applied biases, in contrast with the supra-linear trend of gold-based transistors. Moreover, short channel effects are considerably suppressed in graphene electrodes devices. More specifically, current on/off ratios independent of the channel length (L) and enhanced response for high longitudinal biases are demonstrated for L down to ~140 nm. These results are rationalized taking into account the morphological and electronic characteristics of graphene, showing that the use of graphene electrodes may help to overcome the problem of Space Charge Limited Current (SCLC) in short channel OFETs.