Ms Grahame launched a petition in August to secure fuel price derogation, which would see Borderers paying the same for fuel as the rest of the UK.
Ms Grahame said: “Hundreds of people have already signed the petition and I would encourage people to keep doing so as when VAT goes up in January people in the Borders will be faced with major increases again.
“While the Treasury makes millions from soaring revenues more and more businesspeople, farmers, fishermen and families in our region are finding themselves out of pocket so I would urge people to contact my office and sign the petition.”
An announcement was made this week that a pilot scheme to cut fuel duty by 5p per litre in the Inner Hebrides, Outer Hebrides and the Northern Isles and Ms Grahame would like to see the scheme extended to the Borders.
She added: “The region is similar to the Islands in that people here are entirely reliant on private transport so we must make a move towards them not paying more tax than anywhere else in the UK.
“I’ve long campaigned for a reduction in fuel duty in the Borders and I would urge Michael Moore MP to help the fragile economy of the region by introducing the scheme here too.”