A YouGov Poll for the British Heart Foundation Scotland shows 70% of people in Scotland would support changing the law to an opt-out rather than opt-in system.
It comes as the issue is being debated by MSPs in Holyrood today.
The bill is expected to be passed as the majority of MSPs and the Holyrood health committee back the change.
If the law is changed, it will be assumed that everyone is an organ donor unless a person states otherwise.
This has been the policy in Wales since 2015 and England has already begun the process to make the change as well.
Mid Scotland and Fife SNP MSP and Cabinet Secretary for Social Security and Older People Shirley-Anne Somerville says: