If passed by Congress, the relief package would include $1tn for households, with direct payments of $1,400 to all Americans.
The relief proposal includes $415bn to fight the virus and $440bn for small businesses.
Mr Biden, a Democrat, has promised to beat the pandemic that has killed more than 385,000 people in the US.
He campaigned last year vowing to do a better job handling the virus than outgoing President Donald Trump, a Republican.
The direct payments of $1,400 would come on top of $600 payments provided in a relief bill enacted last month.
Mr Biden’s proposal comes as a winter surge of the corona virus breaks records.
Each day brings well over 200,000 new cases in the US and the daily death toll sometimes tops 4,000.
In a prime time speech on Thursday night from his hometown of Wilmington, Delaware, he said: “A crisis of deep human suffering is in plain sight and there’s no time to waste.”
“The very health of our nation is at stake,” he added. “We have to act and we have to act now.”
The incoming president said: “There will be stumbles, but I will always be honest with you about both the progress we’re making and what setbacks we meet.”
Mr Biden wants to pump $20bn into vaccinating Americans, including setting up mass vaccination hubs and dispatching mobile units to remote areas.
Two effective vaccines were delivered under the Trump administration, but health officials say the rollout needs to speed up.
“The vaccine rollout in the United States has been a dismal failure thus far,” said Mr Biden. His administration aims to deliver 100 million jabs in 100 days.
So far, about 11 million doses of the vaccine have been administered in the US, according to the Centers for Disease Control and Prevention (CDC).
His plan also calls for $50bn to expand testing and $130bn to help most schools reopen by the spring.
The plan would fund the hiring of 100,000 public health workers for contact tracing.