The Pensions Bill plans a new single-tier state pension for people reaching the age on or after April 6, 2016.
Age UK said that while the changes will help many women, others will lose out.
It said estimates show 40,000 people reaching state pension age in the first five years of the new system will have a lower state pension as a result, and nearly 30,000 of them will be women.
Research by the charity found 79% of 2000 people aged over 50 oppose it.
It will be based on individual qualification, so people will not be able to inherit or derive rights to the single-tier pension of their spouse.Caroline Abrahams, charity director at Age UK, said: "The aim of this reform is to introduce a fairer state pension yet it cannot be fair to change the rules without giving people enough time to also change their plans."
A Department for Work and Pensions spokeswoman said: "We are creating a state pension that is fit for the 21st century.
"Women will particularly benefit from the new flat rate state pension, with around 650,000 reaching retirement in the 10 years after it is introduced benefiting by on average £8 a week."