Talking exclusively to the Express.co.uk, the new Ukip leader said he was looking to get at least into “double figures” of the amount of MPs into the House of Commons.
Mr Nuttall said: “In terms of electoral success, I will be a leader who focuses on election and by-elections and Parliamentary elections.
“My hope, and I envisage, that we will get double figures elected to the House of Commons come 2020.”
The 39-year-old – who cruised to victory after winning 62.6 per cent of election vote – mooted that Mr Farage will stand as the Ukip candidate if there was a by-election in Thanet.
Mr Farage has been tipped for a peerage following June 23 vote to leave the EU and received a glowing endorsement from Donald Trump to be the UK’s next US Ambassador, with the President-elect tweeting he would make a “great” candidate for the job.
But on both his own electoral ambitions and that of the former leader, Mr Nutall said: “If there’s a Thanet by-election, Nigel Farage will be our candidate.
“I may well be a candidate at a by-election myself within the next two years.”
Despite receiving just shy of four million votes in the last general election, Ukip only managed to clinch one seat in the House of Commons.
In comparison, the SNP snagged 1.4million votes and has 56 seats in Westminster – and the new leader is looking to overthrow the outdated electoral system to help reflect the opinions of British people.
He said: “The voting system is an absolute disgrace. It cannot be right that our party gets four million votes and comes back with one MP.
“The first past the post system has no place in a 21st century western functioning democracy. It needs to be changed and we will campaign to have that change.
“At the same time we will also campaign to do away with postal voting on demand which allows for electoral fraud voting on an industrial basis.”
Mr Nuttall, who based his campaign around being the “unity candidate”, said he had received a warm reception as party leader and that while the party was in an “existential crisis”, his election marked a new chapter in the party’s history.
The Bootle native added: “The reaction has been great, particularly amongst Ukip members. It’s the biggest mandate that anyone has achieved within the party and my call for unity has obviously resonated.
“People have realised that we have been in an existential crisis and now it’s time for everyone to come together and put the cause first.
“I think we’re in a far more positive position now than we were yesterday.”