Video report by Rajiv Popat
More than 120 graves dating back hundreds of years have already been found, and archeologists believe there could be up to 600 in total.
In an interview with ITV News Central, Matthew Morris an rchaeologist from the University of Leicester said: "It's a fantastic opportunity this, to learn more about the people of Leicester.
"Getting this snapshot of an entire generation after generation of people from Leicester is going to be really fascinating.
"We have had lots of skeletons obviously of those individuals, some of them have been buried in quite ornate coffins, some of them have had name plates that we have been able to read and put names to some of the individuals which is really quite unusual."
One of those was a woman called Anne Barrat who was born in 1786.
Anne was one of eight children, and her entire family were buried on the Cathedral grounds.
Mr Morris added: "We know her father was a wealthy hosier in the town, so sort of the staple industry in that period.
"She died in 1855, and... From her will she left quite a lot of charitable donations to the royal infirmary and to other schools."
Once all of the remains are recovered, they will be taken away and analysed.
They will then be brought back to the cathedral to be re-buried.
As the archeologists dig deeper, they're expecting to find some interesting pieces of roman archeology.
The remains of King Richard were found by members of this excavation team in a council car park in Leicester in 2012. He was later reinterred inside the cathedral.