Those travelling on a train from the west and south-west of Scotland currently have a choice of disembarking at Glasgow Central and walking to Queen Street, or changing at Carstairs to travel on to Edinburgh and the east.
Mr Brown told MSPs at Holyrood that plans are under way for a single Kilmarnock to Edinburgh train via Glasgow Central, but he rejected renewed calls to revive the potentially costly and disruptive Glasgow Crossrail link between Central and Queen Street.
Kilmarnock SNP MSP Willie Coffey said: "A large population lives west and south-west of Glasgow, but the economic opportunities available to my constituents to travel and work in Scotland's capital are hampered by having to change trains and stations and walk between Glasgow Central and Queen Street, meaning the travel time can be around two hours to travel a distance of 60 miles.
"Is there any hope that a through service will become available for customers from the south-west of Scotland at any point in the future?"
Mr Brown said: "The Scottish Government has already improved rail services from areas to the west and south-west of Glasgow, with passengers now able to travel to Edinburgh via Shotts and Carstairs services from Glasgow Central.
"The Paisley corridor rail improvements have also increased capacity and improved journey quality for the busiest sections of the Scottish network.
"Additionally, through the provision of a longer franchise, we are seeking the next franchisee to develop opportunities and strategies for delivering innovative enhancements to train services.
"There is work ongoing in relation to getting from Kilmarnock to Glasgow Central and staying on the same train to Edinburgh in relation to the new franchise.
"It might be an idea for Willie Coffey to engage with the potential bidders for the new franchise to make sure that they are well aware of the aspirations of his constituents."
Central Scotland Labour MSP Mark Griffin asked about any plans to revive the shelved Glasgow Crossrail project to link the two main stations.
Mr Brown said: "The Government doesn't support the scheme. We believe it would disadvantage many existing passengers by diverting existing services from the city centre stations to run via Crossrail. It would substantially increase the subsidy requirements through the addition of new services and increased infrastructure investment at critical points elsewhere on the network.
"We estimated in 2008 that the cost of this would be between £150 million and £250 million."