Despite Mr Smith claiming to be more "electable" than his rival, members, union affiliates and registered supporters are flocking to Mr Corbyn's campaign.
A YouGov survey for The Times of those entitled to vote in the contest puts the current Labour leader on 62% with Mr Smith trailing on 38%.
Mr Corbyn received just shy of 60% of the vote when he was elected to the job in September 2015.
The new poll gives a boost to Mr Corbyn's campaign ahead of another leadership debate in London tomorrow.
Today Mr Corbyn will make a speech highlighting his policies on women's issues.
Mr Smith, meanwhile, has said he believes Labour must be pro-immigration, even if it means losing votes to Ukip.
In an interview with The Independent he said “some electoral damage” should not prevent Labour from championing the benefits of immigration.
Mr Smith's comments could unnerve Labour MPs whose constituents backed Brexit, however today's poll will do little to sway the 172 LabourMPs who backed a no-confidence motion in Mr Corbyn - a move which ultimately led to Mr Smith's challenge.
The poll puts Mr Corbyn ahead in all three groups of people who are eligible to take part in the vote.
It found that 52% of full members intend to back Mr Corbyn compared to 40% for Mr Smith.
Meanwhile, among registered supporters it was 70% to 25% in favour of Mr Corbyn.
Mr Corbyn also has the backing of the union affiliates by 54% to 33%.
An estimated 640,000 members and supporters have been tasked with choosing between the pair.
Voting in the contest is already under way with a winner to be announced on September 24.
from Instituto Manquehue - rss http://ift.tt/2bYTD09