The overall market last month fell by 8.5% compared to the same period last year, while Hyundai registrations were down just 2.2%.
Allan Rushforth, senior vice president and COO of Hyundai Motor Europe, commented: "Our plan for this year is to stabilise the 3.5% market share we gained in 2012, so we're encouraged by the positive start in January.
"Following an intensive product launch period in which we introduced 15 new models to the European car market in five years, our aim for 2013 was to consolidate our position and strengthen the fundamentals of our business through qualitative growth.
"Therefore, as well as maintaining our European market share, we're focusing on enhancing the Hyundai brand image and increasing customer satisfaction in order to improve retention rates - we're determined to keep the customers we worked so hard to win in recent years."
Hyundai is investing significantly in its European operations this year, in order to build a solid foundation for future growth.
The company plant in Turkey is currently undergoing a €475 (£410) million investment to increase its annual output potential from 120,000 to 200,000 cars a year. The company's headquarters are also undergoing expansion, while a €5,5 (£4.7) million test centre located next to the famous Nürburgring race track in Germany will allow the quality and driving performance of Hyundai's European-designed vehicles to be further improved.