Olmert is already facing 18 months in prison for a separate conviction on bribery, which he will begin on February 15.
Today's hearing was over Olmert's May 2015 conviction at the Jerusalem District Court of fraud and corruption for receiving envelopes of cash from a US businessman while trade and industry minister in the early 2000s.
The appeal was over "the conviction and the punishment" as well as "the decision it will be consecutive and not concurrent," a lawyer for Olmert told the panel of five justices.
"A person committed two felonies. Why would he get some kind of discount," he asked.
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Olmert appealed to the judges to take into consideration the difficulties he had faced over the years of investigations and trials, comparing the experience to facing a tennis ball machine firing balls "at high speed in all directions and you have to react to each ball, that's how I feel."
The court did not issue a decision, nor did it say when it would rule on the appeal.
On Monday, 70-year-old Olmert struck a deal with the prosecution over two charges of obstructing justice, according to which Olmert will concurrently serve six months for obstructing justice with his 18-month sentence for corruption in return to confessing to the felonies.