A new and complete version of the   L k transition model has been continually developed and proposed in the present paper. This version of the   L k transition model can predict the effects of pressure gradient on the mean flow. The   L k transition model is validated with the ERCOFTAC T3-and T3C-series experimental data of Coupland [1]. The validation shows that the computed results of the   L k transition model are in good agreement with the experimental data. The performance of the   L k transition model is assessed in comparison with those of the L k transition model of Walters and Cokljat [2], the    Re transition model of Langtry and Menter [3], and the  transition model of Ge et al [4] in case of the transitional flow through the compressor blade passage of Zaki et al [5]. It is found that the proposed   L k transition model is the only transition model that can consistently capture the separation bubble on the compressor blade.