Hallmark cards is set to lay off 300 printing staff from its Braford plant by the end of the year.
The American company will be outsourcing its printing operations to the US and Far East.
Distribution and design jobs look to be safe, with no layoffs planned at its Brighouse distribution centre.
Chris Daly, regional officer for UNITE union, said: “We want to know from the company what the business case is for the closure of printing in the UK to see if we can put alternatives forward to try and keep as many jobs in the area as we can.
“It’s frightening - it seems that they don’t want to produce this sort of stuff in the UK anymore.
“It’s bad for the country as well as for the individuals and families affected - we’ll be in a position where we’ll be importing something that we used to produce.”
Steve Wright, international CEO of Hallmark, said: “We fully recognise how hard this decision will be on those of our employees who are affected. We will make sure that we support our people throughout, working closely with them to look for every opportunity to minimise job losses and, where this is not possible, to support employees in finding new employment.
“The essence of our company is design and creativity. By outsourcing manufacturing, we are making a strategic decision to focus our UK business on what we do best, while at the same time reducing costs, ensuring that the business is best placed to grow and thrive.
“Having been based in Bradford for more than 30 years, we’re as committed to the city as ever. While this is an extremely tough decision, our intention is to build a business that can continue to contribute positively to Bradford’s economy and its people.”