Paul Hudson said the error may have crept into the computer's climate model as a result of successive years of milder weather.
His claim was rejected by the Met Office but other experts said there could be flaws in the system, which was first developed 50 years ago.
In a blog
, the BBC Look North presenter writes: 'Clearly there is the rest of January and February to go, but such has been the intensity of the cold spell...it would take something remarkable for the Met Office's forecast (of a mild winter) to be right.
'It is also worth remembering that this comes off the back of the now infamous barbecue summer forecast.
'Could the model, seemingly with an inability to predict colder seasons, have developed a warm bias, after such a long period of milder than average years?'
The Met Office produces its forecasts by feeding information from sources, including satellites and weather stations, into a 'climate model'. A set of complex equations then predict weather changes.
Mr Hudson appears to be suggesting that data recorded over the past decade of warmer winters could be unduly influencing the computer's calculations. However, the Met Office denies this, saying 'any small biases' are automatically corrected before it issues seasonal forecasts.
A BBC weather forecaster has suggested that the Met Office's super-computer has a 'warm bias' which has stopped it predicting bitterly cold spells like the one we have just endured.