Toyota was the first company to market a modern hybrid car in Japan beginning in 1997, but Honda beat them to the US market by a few in 1999. The Honda Insight was and remains Honda's only dedicated hybrid model, with all the others being based on existing Honda models. The aluminum bodied Insight was never a huge seller and production of the first generation model ceased in 2006.
British magazine AutoCar is reporting that Honda will be showing off a new dedicated hybrid concept at the Geneva Motor Show in early March. In typical Honda fashion this will be a thinly disguised version of a new production successor to the Insight. The new car is expected to be similar in size to the Civic and priced lower than the Prius. No technical details are available right now, but a lower price indicates that it will probably continue with an evolution of the current Honda Integrated Motor Assist system. On the other hand, plug-in hybrids seem to be all the rage this week, so it wouldn't be surprising to see Honda build a PHEV and be first to market, even at a loss. This would also make more sense for a dedicated platform.