An evaluation of the capability of low-Reynolds-number k-ε turbulence models and an approach for improving the models to predict transition in external boundary layer flows subject to free-stream turbulence are presented. By comparing calculations of a number of transitional boundary layers by five k-ε models(Jones-Launder, Launder-Sharma, Nagano-Hishida, Nagano-Tagawa, Yang-Shih), Launder-Sharma model is selected as a best performaning one and it is employed in a series of computational tests to examine the ability of this model for reliable prediction of transitions. Modifications are proposed in source terms of ε-equation proposed by Launder-Sharma model. A near-wall modifications is also made to k-ε-γ model. It is found that these modifications lead to improved predictions of transitional boundary layers. The fact that the latter shows better performance than the former in transition onset and length suggests that intermittency factor must be taken into account in the laminar to turbulent transition modelling.