The demand for models of LIKEaBIKE has seen the Tadcaster-based operation of the same name double its number of UK-wide distributors from 50 to 100 in the last year.
LIKEaBIKE is planning to move to a larger showroom at the Thorp Arch Trading Estate near Wetherby.
The LIKEaBIKE was being tipped as the must-have gift for children between the ages of two and six because it gives them an easy and safe introduction to the world of cycling.
According to the manufacturers, the bike helps make the transition to a more conventional cycle much easier and more natural.
The man behind the product, Rolf Merten, realised there was a gap in the market and believed normal children's bicycles, with pedals and stabilisers, not only obstruct children learning to ride, but teach them how to pedal and not how to balance.
The Yorkshire company is run by John Stainthorpe, who started the business after working with his father at Cycle Sense, a bicycle shop based in Tadcaster.
The 22-year-old sales manager from Thorp Arch said the product caught his eye six years ago at a cycle show when children were fighting over the bikes.
Mr Stainthorpe said: "I think it was a matter of being in the right place at the right time.
"I thought the LIKEaBIKE was highly original and a great way of teaching children how to cycle. It keeps the children active and away from the television. I therefore signed a contract as soon as I could and it has grown from there."
The large range of bikes stocked by LIKEaBIKE are handcrafted from natural materials including birch and beech plywood and also aluminium.
They are made by Kokua Holzpielzeug, a small family business in Roetgan, Germany, and despite weighing only 3.5 kg are designed to be durable enough for young children.
The word Kokua across the bikes is a Hawaiian word emphasising the bikes philosophy meaning 'in harmony'.
The parent company is 10 years old this year and although the UK franchise is only two years old, Mr Stainthorpe believes the concept has been quick to gain admirers.
He said: "The ball has started to roll of late and we haven't spent a penny on advertising, it has all been through word of mouth. People have seen children playing on them in the park and have chased after the parents enquiring where they got them from."
The popularity of the bike has even surpassed Mr Stainthorpe's expectations, who said he had been "blown away by the Christmas demand".
The inspiration for the LIKEaBIKE dates back to a 'walking machine' invented by the German Baron Karl Drais von Sauerbronn in 1817.
The machine supported his body weight whilst enabling him to move around on two wheels with the front one steerable and the device was propelled by pushing the feet against the ground to create forward motion in the form of a gliding walk.
There are plans for new models next year and there is even an adult-sized bike in the pipeline.