Francesco Schettino was given 16 years in jail last year, after a court found him guilty of manslaughter, causing a maritime accident and abandoning ship.
At the trial in Florence, he is seeking to overturn the conviction, while the prosecution seeks a longer prison term.
The Costa Concordia capsized after it hit rocks close to Giglio island.
On Thursday, lawyers of the 55-year-old captain are expected to argue that the disaster off Tuscany's coast was a collective failure of the ship's crew and others should share the blame for the disaster.
"We will ask that the responsibility of all the protagonists in this affair be redefined, not just that of our client," lawyer Donato Laino told the AFP news agency.
Salvaging the Costa Concordia
Schettino, who has not yet begun his sentence, also denies that he abandoned ship before passengers and crew had been evacuated.
Meanwhile, the prosecution is seeking a 26-year prison term.
If Schettino loses his appeal, he can try again at Italy's highest court - the Court of Cassation.
In February 2015, he was sentenced to 10 years for multiple manslaughter, five years for causing the shipwreck and one year for abandoning his passengers.
Investigators had severely criticised his handling of the disaster, accusing him of bringing the 290m-long vessel too close to shore when it struck the rocks.
More than 4,000 passengers and crew were forced into a chaotic evacuation.
During the trial, Schettino said he had taken the ship so close to land for "commercial reasons" in a bid to please his passengers and those ashore.
He had also rejected rumours that he had wanted to impress his lover, Domnica Cemortan, who was with him at the helm.
Costa Crociere, the company that owned the ship, sidestepped potential criminal charges in 2013 by agreeing to pay a â‚¬1m ($1.1m; Â£779,000) fine.
It is being sued by survivors, the Tuscany region and Giglio island for further damages.
Five other employees, including the helmsman, were handed prison sentences ranging from 18 months to two years and 10 months in plea bargains concluded early in the investigation.

The artificial intelligence system - LipNet - watches video of a person speaking and matches the text to the movement of their mouths with 93% accuracy, the researchers said.
Automating the process could help millions, they suggested.
But experts said the system needed to be tested in real-life situations.
Lip-reading is a notoriously tricky business with professionals only able to decipher what someone is saying up to 60% of the time.
"Machine lip-readers have enormous potential, with applications in improved hearing aids, silent dictation in public spaces, covert conversations, speech recognition in noisy environments, biometric identification and silent-movie processing," wrote the researchers.
They said that the AI system was provided with whole sentences so that it could teach itself which letter corresponded to which lip movement.
To train the AI, the team - from Oxford University's AI lab - fed it nearly 29,000 videos, labelled with the correct text. Each video was three seconds long and followed a similar grammatical pattern.
While human testers given similar videos had an error rate of 47.7%, the AI had one of just 6.6%.
The fact that the AI learned from specialist training videos led some on Twitter to criticise the research.
Writing in OpenReview, Neil Lawrence pointed out that the videos had "limited vocabulary and a single syntax grammar".
"While it's promising to perform well on this data, it's not really groundbreaking. While the model may be able to read my lips better than a human, it can only do so when I say a meaningless list of words from a highly constrained vocabulary in a specific order," he writes.
The project was partially funded by Google's artificial intelligence firm DeepMind.
The appeals trial is to begin in Italy of the captain held responsible for the Costa Concordia cruise ship disaster in 2012, in which 32 people were killed.
[NEXT_CONCEPT]
Scientists at Oxford University have developed a machine that can lip-read better than humans.