At a speech in Strasbourg, David Cameron will use the UK's presidency of the Council of Europe to push for change.
He has clashed with the European court over a number of issues including the deportation of criminals and whether prisoners should be allowed to vote.
However, all 47 countries must sign up to the reforms if they are to be enacted.
The Prime Minister is expected to say: "The Court should be free to deal with the most serious violations of human rights; it should not be swamped with an endless backlog of cases.
"The Court should ensure that the right to individual petition counts; it should not act as a small claims court.
"And the Court should hold us all to account; it should not undermine its own reputation by going over national decisions where it does not need to."
The European Court currently has a backlog of 150,000 cases. Last year 950 decisions were made on British applications but only eight resulted in a violation.
Downing Street sources told Sky News there is broad agreement on the problem, but the 47 countries of the Council of Europe now need to agree on the solution.
They admit this will be difficult, saying "we don't underestimate the scale of the challenge".
David Cameron will set out his vision of a reformed Court by saying: "This is the right moment for reform - reforms that are practical, sensible and that enhance the reputation of the Court. So we are looking to improve the efficiency of the Court.
"New rules could enable it to focus more efficiently and transparently on the most important cases.
"We want to improve the procedures for nominating judges. The Assembly needs consistently strong shortlists from which to elect judges - and clear guidelines on national selection procedures could help with that.
"And we are hoping to get consensus on strengthening subsidiarity - the principle that where possible, final decisions should be made nationally."
ECHR judge Sir Nicolas Bratza QC
It is disappointing to hear senior British politicians lending their voices to criticisms more frequently heard in the popular press, often based on a misunderstanding of the court's role and history and of the legal issues at stake.
The speech will be welcomed by Conservative backbenchers who want a renegotiation of Britain's relationship with Europe.
Liberal Democrats are also believed to agree the court needs reforming - although they support the European Convention of Human Rights.
In Tuesday's Cabinet meeting, the Deputy Prime Minister Nick Clegg told MPs they could count on Lib Dem support, adding: "If you are a defender of human rights then you want to see this court working properly."
Mr Cameron will also emphasise his commitment to human rights: "Human rights is a cause that runs deep in the British heart and long in British history…It was that same spirit that led to the abolition of slavery, that drove the battle against tyranny in two World Wars and that inspired Winston Churchill to promise that the end of the 'world struggle' would see the 'enthronement of human rights'.
"These beliefs have animated the British people for centuries - and they animate us today."
Ahead of the speech, the court's top judge Sir Nicolas Bratza QC hit out at the Prime Minister.
Writing in The Independent, he said: "It is disappointing to hear senior British politicians lending their voices to criticisms more frequently heard in the popular press, often based on a misunderstanding of the court's role and history and of the legal issues at stake."
He said it was "particularly unfortunate" that the prisoner voting issue "has been used as the springboard for a sustained attack on the court and has led to repeated calls for the granting of powers of Parliament to override judgments of the court against the UK, and even for the withdrawal of the UK from the [Human Rights] convention".