The party argues that a charge could lead to two billion fewer cups being used every year.
The Lib Dems have pointed to the impact of a 5p charge on plastic bags, which has led to a big reduction in use.
And they announced that delegates at the party's annual conference will pay a 5p charge on disposable cups.
"Throwaway cups are a threat to wildlife and the environment and it's high time the government stepped in to reduce the amount of waste created each year," said Lib Dem leader Tim Farron.
"I want to see a culture shift towards bringing your own cup for a refill, rather than buying cups which are often non-recyclable and then throwing them away."
Since October 2015, shoppers in England have been charged 5p for every new plastic bag they use at large stores.
The charge applies only to shops or chains with 250 or more full-time employees, with the proceeds donated to charities and other causes.
In July 2016 the government estimated the charge would result in six billion fewer plastic bags being used during the year and Â£29m had been raised.
Wales introduced a levy in 2011, followed by Northern Ireland in 2013 and Scotland in 2014. They saw reductions in bag use of 76%, 71% and 80%, respectively, in the first year after the fee was established.
The Lib Dems said 2.5 billion disposable coffee cups were used each day and fewer than one in 400 were recycled.
The party has not said whether its proposed charge would apply just to larger businesses, in line with the carrier bag charge, or to all businesses, but it is not waiting for a change in the law to impose a 5p charge on disposable cups used at its annual conference in September.
The Liberal Democrats have called for the introduction of a 5p charge on disposable coffee cups to cut usage across the UK.