In January the number of transactions made via smartphone rose 96%, while the number made by tablet rose just 13%.
Tina Spooner, chief information officer at IMRG, said consumer confidence in using smartphones for shopping was "most likely boosted by the design shift toward larger screens, together with improved retailer mobile sites".
She added: "Conversely, growth in sales completed on tablet devices fell below the overall online growth rate."
Online retail grew by 15% annually in January, compared to just 7% in January 2015.
The strong performance suggests that the 'Black Friday effect' – which appeared to influence a lingering downturn in sales growth in the first quarter last year – has not been repeated this year.