Jeremy Ludowyke, the principal of Melbourne High School, a selective secondary school for boys, said that he was considering pushing back the school start time to 9.30am rather than the current 8.50am.
"There is a good research base to say we probably ask students to start their working day a little earlier than they should," he told the Herald Sun.
Although this would mean students finishing later, longer sleep patterns have been shown to have educational and health benefits for teenagers.
Earlier this year, Steven Lockley, an associate professor of medicine at Harvard Medical School, told the ABC that there are many positives to later school start times.
"Pushing school start times later, which has happened in a number of cases, has been shown to benefit the educational attainment of the children, but also behavioural outcomes, things like less truancy," he said.
"And we even think there are some improved risks of some more serious disorders such as mental health problems, depression and even suicide risk in teenagers, along with more sleep and better bedtimes. And so, this is a serious matter. It's not just about lazy teenagers falling asleep. They are doing themselves harm by having to do this each and every day."
Researchers at the Bradley Hasbro Children's Research Center in Rhode Island studied the impact of a 25-minute delay in school start time on teenagers and found that students' overall sleep time increased by an average of 29 minutes.
The study also found that students experienced significant reduction in daytime sleepiness and improvements to mood and focus.
Templestowe College - another school in Melbourne - has already adopted a later time schedule. Next year, students will able to select their school times: 8.50am-3.30pm, 10.30am-5.15pm or 7.15-1.15pm.