He told members that "every power and every pound" at his disposal had been used to move Scotland forward.
Mr Swinney added that First Minister Nicola Sturgeon was "by and far the best" person for the role.
The two-day conference in Glasgow is taking place ahead of the Scottish Parliament election on 5 May.
In his opening speech, Mr Swinney posed the question: "Can anybody seriously imagine the other party leaders in Scotland so effectively standing up for Scotland?"
He added: "A couple of weeks ago the prime minister came up to Scotland and talked about how much he feared an SNP victory in May.
"It seems that the Tories don't like having a government in Scotland which stands up to them.
"Now I think that's good reason enough for us to get out there and campaign for a strong SNP victory."
The SNP has been in power in Edinburgh since 2007, with the party first operating as a minority administration before winning a Holyrood majority in May 2001.
Opinion polls north of the border indicate that the SNP is on course to winning a second majority term in the Scottish Parliament.
Mr Swinney said: "Our opponents often say that they want to fight this election on the SNP's record in government.
"But they don't need to worry - we will be talking a lot about our record over the next few weeks. That's for one simple reason, the Scottish National Party in government has record to be proud of."
He added: "When we first took office in 2007, none of us knew that we'd face the toughest recession in living memory, and the harshest Tory austerity.
"But we've used every power and every pound at our disposal to move Scotland forward."
Scotland's Deputy First Minister John Swinney has opened the SNP's spring conference saying his party in government has a record to be proud of.