The rate soared by 221 per cent between July and September last year compared to same period in 2018.
It is now more than twice that of any other British train operator.
Operator Serco received 394 complaints per 100,000 journeys.
The rate also doubled from 206 between April and June last year.
In the latest figures, the next highest was fellow cross-Border operator Virgin Trains West Coast - now Avanti West Coast - with a rate of 170, up 1 per cent on the previous year.
UK Government-run LNER, which operates cross-Border trains on the east coast, was next with a rate of 150, up 28 per cent on 2018.
However, ScotRail complaints were down by 6 per cent to 27 per 100,000 journeys - the lowest of any train firm operating in Scotland.
The Caledonian Sleeper has been set by a catalogue of problems since its new fleet came into service last April on the Edinburgh and Glasgow-London "Lowlander" routes.
They include damaged pipework affecting the new showers, technical glitches locking toilets out of use, poor room cleaning, staff shortages and strikes.
It led to the trains' introduction on the "Highlander" routes between Aberdeen, Fort William, Inverness and London to be postponed.
The Office of Rail and Road regulator, which published the figures today, said: "The delayed introduction of new trains as well as unforeseen problems has meant Caledonian Sleeper has dealt with a larger volume of correspondence in 2019-20 Q2 than in the same quarter last year.
"Long-distance train operators had the three largest complaints rates.
"This trend is consistent with previous data and is representative of the fact long-distance operators receive more correspondence about their services than operators in other sectors."
Scottish Labour transport spokesman Colin Smyth said: "Yet again, we see rail services managed by the SNP government failing Scotland’s long-suffering rail passengers.
"Not only are the SNP failing to hold Serco to account for their failings running the Caledonian Sleeper, but they are rewarding them by trying to hand them a new contract running lifeline ferry services [for NorthLink to the Orkney and Shetland].
"This growing crisis comes after ScotRail’s performance declined to the point where the SNP listened to Labour’s calls to end the failing Abellio franchise.
"They now need to do the same and call a halt to Serco’s mismanagement of the Sleeper services and start to put passengers first."
Ryan Flaherty, Serco’s managing director for Caledonian Sleeper, said: “We are dedicated to enhancing the guest experience and have made great strides in recent months.
"However, we recognise during the period where our new trains were introduced there was some disruption which affected guest journeys.
"We have taken this feedback on board and are already seeing an improvement across a number of areas, with less disruption as a result and are now on track to return to our normal level of high satisfaction.”
A spokesperson for the Scottish Government's Transport Scotland agency, which controls the Sleeper franchise, said: “It is already well-documented the introduction of the new Mk5 vehicles has been difficult for the operator and passengers.
"That is why the roll out of these coaches to the Highlander services was delayed.
"We know the vast majority of the rise in complaints relates to on-train quality issues, which are being resolved.
“We continue to monitor both performance and passenger satisfaction closely.”