I will travelling in Taiwan on January 2014 for around 10days. I wonder what kind of clothes should I bring?

May I know whether you are going for travel in early, mid or late Jan.? Anyway, for the whole month, the lowest temp will be around 9C and highest of 22C, so it won't be taht cold. Cloudy or lightly rainy days would happen then. Therefore, I suggest you take cardigan or light sweater, jacket and jeans as well as umbrella or other rainy gear.

Will be travelling in mid January.

Well then, the average temperature will be around 13C and cloudy days would be the majority. The clothes I mentioned the above may also help.