Shao, who died last June, once said: "If I cannot go to school for classes, my son will come instead."
Mao said he would take his mother's responsibilities to be honorary president of the school and give lessons later.
"People should pay more attention to education for all-round development than for scores. Mao Zedong's Thought should be covered in high schools like Matsuda," Mao said, adding that he is in discussions with the vocational school to give classes of Mao Zedong's Thought soon.
Mao, who feels that upholding Mao Zedong Thought is his unshakable responsibility, has authored a number of books, including the award-winning My Grandfather Mao Zedong.
"It was after joining the army that I began to really understand my grandfather. As a soldier, I regard him as our leader and commander-in-chief," he said.
Mao also suggested his grandfather's birthday and the day of his death become a legal national holiday in commemoration, the report said.
The proposed dates are Dec 26 when his grandfather was born and Sept 9 when he died.
"As long as we have special holidays for our traditional events like the Dragon Boat Festival and the Mid-Autumn Festival, the country should also set up similar holidays for important dates like the birthday or the day of death for great leaders," Mao said.
He added that he will propose the idea to next year's annual session of the CPPCC.
Mao said he will show up in Tian'anmen Square on Oct 1 to watch the National Day parade celebrating the 60th anniversary of the People's Republic of China.