This was for killing his girlfriend Reeva Steenkamp and will now seek a murder conviction.
The Olympic and Paralympic athlete, whose lower legs were amputated as a baby, killed Steenkamp on February 14 last year by firing four 9mm rounds into the locked door of a toilet cubicle in what he said was the mistaken belief an intruder was hiding behind it.
(READ MORE: Pistorius not guilty of murder)
During the seven-month trial, the state failed to convince Judge Thokozile Masipa, 67, of Pistorius' intent to kill when he fired, leading to his conviction for negligent killing - culpable homicide - and a five-year jail term in October.
State prosecutor Gerrie Nel said in his application to appeal on Tuesday that the judgement was "shockingly inappropriate" and requested permission to seek a murder conviction, which would carry a minimum 15 year jail term.
Nel argued that even if Pistorius did not know Steenkamp was behind the door when he fired, the athlete showed intent to kill whoever was in the small toilet cubicle.
"I cannot say the prospect of success at the Supreme Court is remote," Judge Masipa said in granting the appeal.
(READ MORE: Judge Masipa slams Pistorius with five year prison sentence)
Masipa dismissed the state's application to appeal the five- year prison sentence, meaning Pistorius' jail term will not be extended unless the state convinces the Supreme Court of Appeal to overturn the original culpable homicide verdict.
Her decision to rule out murder was criticised by several legal experts and the Women's League of the ruling African National Congress (ANC) as an erroneous interpretation of the law.