Pollsters found that 63 per cent support the move, while 24 per cent have no view and three per cent are unsure of their opinion.
The poll, which was not commissioned by any body external to YouGov, comes shortly after heated debate about women bishops at the Church of England's General Synod.
Supporters of openly gay bishops also outnumber opponents. Thirty-nine per cent say they are in favour, with 27 per cent against.
In addition, 31 per cent have no opinion, while three per cent say they don't know.
The figures are likely to reinforce the popular perception that Christians are reactionary and reluctant to change.
Christians who support sexual inclusion argue that churches should be at the forefront of social change, not struggling to keep up.
The researchers found that women were more likely than men not only to support women bishops, but also to support gay bishops.
Tory voters turned out to be less keen on either idea than Labour and Liberal Democrat voters.
Only 58 per cent of Tories said they supported women bishops, compared to 70 per cent of Labour and 73 per cent of Liberal Democrat voters.
SIC: Ekklesia