Onset of initial morphological instability is predicted by using a new analytic model and quantitative phase held model during the solidification of the welding pool of Al-Cu alloy under transient conditions. In the linear growth stage of the welding pool, the dynamic evolution of the interface instability is analyzed, and the interface behaviors under infinitesimal fluctuations are also investigated. The results show that the mean wavelength at the crossover time evaluated from this analytic model is in good agreement with those obtained by the quantitative phase field simulations and the experiments. The linear growth stage takes up quite a long time of the whole solidification of welding pool and thus it should be primarily considered in investigating the transient growth of welding pool. This study establishes a valid numerical framework for studying the dendrite growth under transient solidification conditions and provides a new approach for studying he transient solidification of welding pool. (C) 2014 Elsevier By. All rights reserved.