Transition prediction is a hot research topic of fluid mechanics. For subsonic and tran-sonic aerodynamic flows, eN method based on Linear Stability Theory (LST) is usually adopted reli-ably to predict transition. In 2013, Coder and Maughmer established a transport equation for Tollmien-Schlichting (T-S) instability so that the eN method can be applied to general Reynolds-Average-Navier-Stokes (RANS) solvers conveniently. However, this equation focuses on T-S insta-bility, and is invalid for crossflow instability induced transition which plays a crucial role in flow instability of three-dimensional boundary layers. Subsequently, a transport equation for crossflow instability was developed in 2016, which is restricted to wing-like geometries. Then, in 2019, this model was extended to arbitrarily shaped geometries based on local variables. However, there are too many tedious functions and parameters in this version, and it can only be used for incom-pressible flows. Hence, in this paper, after a large amount of LST analyses and parameter optimiza-tion, an improved version for subsonic and transonic boundary layers is built. The present improved model is more robust and more concise, and it can be applied widely in aeronautical flows, which has great engineering application value and significance. An extensive validation study for this improved transition model will be performed.