Party leader Pedro Sanchez has been acting prime minister since April when PSOE finished first in an inconclusive national election. Last week he lost two investiture votes after talks with far-left party Podemos broke down. He now has until mid-September to break the political deadlock or face a fresh election in November
The poll by the Centre for Sociological Research (CIS) put PSOE 41.3%, up from 39.5% the previous month and a large jump from the 28.7% the party obtained at the election in April.
The last time a single Spanish party secured a parliamentary majority was in 2011, when Mariano Rajoy's Partido Popular won 44.6%.
CIS said the latest survey represented direct voter intentions and lacked the checks and balances used in compiling projections, which were generally more accurate. It polled nearly 3,000 people over the first ten days in July, so before the investiture votes.
PSOE have said they will keep working with all parties to avoid a repeat election - which would be Spain's fourth in as many years - but were no longer prepared to offer a coalition government to Podemos. In the poll, Podemos inched 0.4 percentage points higher to 13.1%, just behind the PP, in second place on 13.7% and unchanged from June.
Ciudadanos (Cs) fell to 12.3% from 15.8% and far-right Vox to 4.6% from 5.1%.
Both the PP and the Cs and have ruled out support for a Sanchez government.
Sanchez became prime minister in June 2018 after Rajoy was ousted in a parliamentary vote of no confidence.
