Dr David Rosser, chief executive of University Hospital Birmingham NHS Foundation Trust, made the warning despite falling cases.
The health chief said it was "really important" people didn't think the pandemic is over as hospital admissions in the region decline.
Dr Rosser, head of the trust which runs Queen Elizabeth Hospital in Birmingham, said: "We're seeing the numbers drop significantly in the organisation which gives us some respite from the peak we had a few weeks ago – which was undoubtedly, by some stretch, much more difficult for us to deal with than the first peak for a whole variety of reasons.
"Not least that it was significantly bigger in terms of the number of patients we had in hospital and the number of patients we had in ITU – on the back of nine months where the team has been working incredibly hard keeping up with Covid and trying to keep up with routine work in the meantime.
"It's been really really difficult – we [currently] have 560 patients, Covid patients in the hospital, about 150 in the ITU, and we're in the strange position where emotionally that feels quite good to me, because it was 1,016 patients in the hospital a few weeks ago.
" But of course, rationally, that is still a quarter of our beds occupied by Covid patients that puts an enormous strain on the system."
Dr Rosser said the decline in Covid-19 patients was causing the trust "considerable concern" and warned it could be a repeat of Autumn where numbers dropped after a peak.
He warned the latest peak of the pandemic came when hospitals – across the region – already had a baseline of 450 patients who were being treated by medics.
Dr Rosser added: "It's really important people don't think this is over – it's a long way from being over and if we get another surge on top of where we are now, I think certainly it's difficult to see how the hospital sector will cope with that."
It comes as Clive Wright, Covid-19 Regional Convenor for the West Midlands, revealed there was currently no new cases of the South African variant of the West Midlands – after extensive testing was carried out in Walsall and in Birmingham – but warned case numbers were still high.
He said: "We're seeing lower admissions to hospital but still significant pressure in the NHS especially in the West Midlands. The region has the second highest case rate in England at 181 per 100,000 compared with the national figure of 137.8 per 10,0000.
"Rate of reduction in the West Midlands – over the last seven days – is minus 28 per cent, now less than the national average of minus 29 per cent. But the case rates here are still very high considering we've been in lockdown for several weeks."