Geim had won the Ig Nobel in 2000 from the Cambridge-based magazine Annals of Improbable Research for making a frog levitate by using a magnetic toy.
The Ig Nobels, which are Harvard's humourous take on the more famous and serious Nobel awards, honour achievements that "first make people laugh, and then make them think".
A physicist at the University of Manchester in England, Geim is the first scientist to win both the Nobel and the Ig Nobel prizes.
Geim said he is "actually quite proud of his Ig Nobel Prize," according to his interview with Improbable Research.
He, however, added that he was not sure if he would display both the awards together in his office since "the Ig Nobel Prize is not really something... visually attractive".
"Essentially, Ig Nobel Prize is given for something which forces people to smile. And, that was always the idea behind the flying frog. And... with Nobel Prize, it is quite obvious that, if you are offered, I am not aware about anyone who rejected an offer of Nobel Prize," Improbable Research quoted him as saying on its website.
At the 2000 Ig Nobel award ceremony, Geim had told the audience that levitating a frog had led to lots of requests, including one from the leader of a small religious group in England, "who offered us a million pounds if we could levitate him in front of his congregation to improve his public relations, apparently".
The real point behind the frog experiment was to demonstrate a phenomenon called diamagnetism.
Diamagnetic materials like water are pushed away by magnetic fields, so a really powerful magnetic field can hold up a frog, which is mostly water.
Geim had shared his Ig Nobel award with Sir Michael Berry.
He shared the 2010 Nobel Prize for physics with fellow scientist Konstantin Novoselov for experiments with a super-thin carbon matter Graphene.
Annals of Improbable Research has awarded the annual Ig Nobel prizes since 1991 "to celebrate the unusual, honour the imaginative — and spur people's interest in science, medicine, and technology."