The information services company said the rate of fraudulent applications soared from 81 in every 10,000 during quarter one of 2015, to 151 in every 10,000 applications by the end of quarter two.
It said identity theft was at the heart of these attacks.
In the first quarter, 49% of all current account fraud was identity theft, but by the second quarter, this figure had risen to 69%.
Despite the growth in current account fraud there has also been a sharp decrease in the rate of fraudulent mortgage applications.
Between January and March, the fraud rate stood at 83 in every 10,000 applications, but this had dropped to 70 in every 10,000 in the three months to June.
This is the first time since 2013 the quarterly fraud rate for mortgages has dropped below 80 in every 10,000 applications.
Nick Mothershaw, UK&I director of identity & fraud at Experian, said: “We’ve seen current accounts slowly become the main target for criminals over the past year, but this sudden surge in fraud is alarming and indicative of a widespread organised attack on financial service providers.
“The good news is that these figures relate to detected and prevented fraud so these large scale attacks are being blocked before the damage is done. However, it does reveal the fervour with which fraudsters are targeting current accounts and the dangers for both the individuals whose identities are stolen and the organisations trying to protect them.”
