A clear majority of members passed a motion in "support of the objectives of the Assisted Suicide (Scotland) Bill".
The Bill is currently making its way through Holyrood and would make it legal to help a terminally ill person to die early.
The party's MSPs will still be given a free vote when the Bill comes before politicians later this year.
Elizabeth Wilson, the Lib Dem candidate for Stirling in the general election, told the conference: "I'm speaking in support of this motion because my mother starved herself to death.
"She actually told my brother when he visited one day that she had decided she wasn't going to eat any more. The course of events was she didn't eat, but she drank water for a little while.
"Then when she wasn't able to drink water then the home squirted water into the back of her mouth.
"And it was of course harrowing for us. There could have been an alternative, and it took three weeks."
But former MSP Mike Rumbles spoke against assisted suicide: "I want to get elected back to the Scottish Parliament. I hope this Bill fails, and it will come back to the Scottish Parliament.
"And I want to be there to express a view, but I deeply respect our party policy, and I don't want us to create a party policy that ties our parliamentarians.
"I know it [the motion] says it won't but it will put pressure on parliamentarians because this is what Scottish Liberal Democrats believe."