Members of the Rail, Maritime and Transport union (RMT) and Transport Salaried Staffs Association (TSSA) will walk out on Friday and the following Friday, and on January 5, 8, 26 and 29, saying they want a similar pay rise to one given to drivers.
The company said it will keep the majority of trains running despite the industrial action.
Manuel Cortes, general secretary of the TSSA, said Sir Richard should meet union leaders as a matter of urgency to help resolve the row, adding: "The company is refusing to treat its staff fairly, provoking a strike that will affect services from London to Birmingham, Manchester, Liverpool and Glasgow."
RMT leader Mick Cash said: "All our members are demanding is a suitable and equal offer to that given to drivers to buy out their claim for a reduction in the base working week.
"We have made it clear to the company that the inequality and underhanded approach of Virgin will be fought tooth and nail. We will not accept our members being dealt with less favourably than others.
"The message needs to get through to Sir Richard Branson on his luxury island retreat in the sunshine that those who are financing his lifestyle through their hard graft have had enough and are prepared to fight for justice in their workplaces."
Phil Whittingham, managing director for Virgin Trains on the west coast, said: "The RMT and TSSA leadership is attempting to cause disruption when many will want to travel by train to spend time with loved ones.
"We have explored a generous 3.6% pay increase; however, the unions' leaderships are insisting on 4%, double the 2% average increase seen across the UK this year.
"We know how important it is for friends and families to get together over the festive season, so we will keep the majority of our trains running with fully-trained staff on board and at stations. We remain open to talks with the RMT and TSSA, and urge them to call off these strikes which will cost their members pay for no gain."
Drivers have received a basic pay rise of 3.2%, with an extra payment after agreeing additional productivity measures which were self-funding, said Virgin.