Only 45% of new pensioners will be entitled to the full, new, flat-rate state pension in the first five years of the system, government figures show.
The new state pension, aimed at simplifying the system, will see a single payment of about £150 made to new pensioners from April 2016.
New figures suggest that two million people will not get the full amount.
However, the government has stressed that they will be no worse off than under the current system.
The new flat-rate state pension was unveiled two years ago by the government, and was promised to be a fairer system. This only applies to new retirees from April 2016, rather than the 11 million people who already receive the state pension.
A freedom of information request submitted by investment firm Hargreaves Lansdown reveals that 45% of those retiring between 2016 and 2020 will get the full amount.
Some with a private or workplace pension provision are contracted out of some of the state second pension, which is being integrated into the new flat-rate state pension. This means they will receive a lower amount. Others have a gap in their National Insurance contributions.
After April 2017, people will also have to work longer, making 35 years' worth of National Insurance (NI) contributions, rather than the current 30, to qualify for the full pension.
Anyone who has paid NI for just a few years will not qualify for the new state pension at all. However, some carers receive NI credits despite being out of the workplace.
"The new state pension will ultimately be a simpler and fairer system. However, in the short term it will be complicated and many people are likely to get less than they may expect," said Tom McPhail, of Hargreaves Lansdown.
He said that without a full state pension forecast, some individuals could get a nasty shock.
The Department for Work and Pensions (DWP) said that it was misleading to suggest that some people were missing out on the state pension as nobody would be worse off than they would be under the current system.
The DWP has a state pension calculator that gives a simplified calculation of entitlement.
The figures come as the government unveiled the name and branding of the new pension guidance system to be launched in April.
New pension flexibility will give the option to anyone retiring from April with defined contribution pension savings to take that money as cash rather than have it tied into a annuity.
This impartial advice will be called "Pension wise" and will be run by Citizens Advice and the Pensions Advisory Service. Any imitation of this service will be illegal.
The service will be available online, over the phone or face-to-face. It will not provide investment advice but will outline the financial options available for those approaching retirement.