The Keep Military Museum in Dorchester plans to use the money to convert a bunker into an interactive experience.
It also wants to create an online gallery of Dorset and Devon people who fought in the war, and a room for community talks and school visits.
The Keep is the only military museum for the regiments of both Dorset and Devon.
The museum, which is receiving the money from the Heritage Lottery Fund, houses thousands of original and unique exhibits, including the desk belonging to Adolf Hitler and hundreds of items from WWI.
Curator Colin Parr said they wanted to gather stories from people whose relatives had taken part in the war.
He added: "Our volunteers will create an online history gallery which will include a contributory archive for people wishing to share their history with us."
Nerys Watts, of the Heritage Lottery Fund, said: "All communities living in the UK have been affected by the First World War in some way, either by the events that took place, or by the changes it brought about.
"We are keen to support projects that, like this one, enable local people to understand more about the heritage of the First World War and how it touched and changed their community."

With a theme of 'We are One', the parade was led by Mary Ellen Campbell, Belfast's first openly gay deputy mayor.
The Pride festival, which runs over 10 days, finishes on Sunday.
More than 100 events have showcased the creativity, arts, history and culture of the LGBT community in the city.
Festival goers and musicians gathered in Queen's Square before parading through the city centre.
The 'Pride Village', aimed at families and children, was a smoke and alcohol-free zone.
Custom House Square hosted a celebration concert on Saturday evening.
Sean O'Neill, chair of Belfast Pride, said the event is now one of the biggest in the city.
"It keeps getting bigger every year," he said.
"The point of pride is about visibility - bringing LGBT people on to the streets to challenge stereotypes and making a point that we want to be full and equal citizens with the rest of the city."

Stephen Hammond said job roles would change when the paper system for car tax discs is scrapped in October.
The minister allayed fears about job losses in a letter to Swansea East AM Mike Hedges.
Mr Hedges said the minister's response would "give comfort" to DVLA employees.
Concerns over the future of some of the 5,000 workers at the Driving and Vehicle Licensing Agency centre were raised in October after Chancellor George Osborne's Autumn Statement.
The chancellor announced that the tax disc would be replaced with an electronic system in October 2014.
The new system will allow people to pay the charge by monthly direct debit.
Mr Hedges had written to Mr Hammond asking for clarification of the government's intentions.
In his response to Mr Hedges, Mr Hammond said: "It is likely that the introduction of a direct debit scheme may mean there will be a natural reduction in the amount of refunds received, in addition to the withdrawal of the tax disc.
"This may mean changes to job roles and the need to train on new processes.
"Any reductions in numbers of people needed for these activities will be managed through redeploying to other growth areas of the business."
Mr Hedges welcomed the minister's assurances.
He added: "Whilst disappointed that the changes will reduce the number of job opportunities at the DVLA, I can see the advantages of both paying by monthly direct debits and not having to show a tax disc.
"I am pleased the minister is committed to redeployment rather than redundancies and I am sure this response will give comfort to many concerned DVLA employees."
A Dorset museum has been given a £51,900 grant to help commemorate the outbreak of World War I.
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Thousands of people took part in the Belfast Pride Parade through the city centre on Saturday.
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Staff at Swansea's DVLA offices will be redeployed rather than face redundancy after changes to the way motorists pay their car tax, a UK transport minister has confirmed.