A modified $textsc{k}$-$varepsilon$model is proposed for calculation of transitional boundary-layer flows with changing pressure gradient. In order to develop the model for this problem, the flow is divided into three regions; pre-transition region, transition region and fully turbulent region. The effect of pressure gradient is taken into account in stream-wise intermittency factor, which bridges the eddy-viscosity models in the pre-transition region and the fully turbulent region. From intermittency data in various flows, Narashima＇s intermittency function, F(${gamma}$), has been found to be proportional to $chi$$^{n}$ according to the extent of pressure gradient. Three empirical correlations of intermittency factor being analyzed, the best one was chosen to calculate three benchmark cases of bypass transition flows with different free-stream turbulence intensity under arbitrary pressure gradient. It was found that the variations of skin friction and shape factor as well as the profiles of mean velocity in the transition region were very satisfactorily predicted.