The abutment of Kala Hydropower project, which is located at the middle of Yalongjiang River in Sichuan Province of China, is made of a high rock slope and the slope stability in the period of construction and operation is one of the key technical issues concerned by the designers. The slope stability is directly related to the dam location and project cost. The Finite Element Method (FEM) and Limit Equilibrium Theory (LET) were adopted to analyze the stability of the left bank slope before excavation and during its construction period under several loading conditions and the sensitivity analysis of the different construction schemes, which will be carried out, was conducted. Some conclusions are drawn as follows: Firstly, the safety factor of the slope in the natural state and the reinforcement-excavation state are beyond 1.0,,but, the top part of slope exceeding the excavating range is 0.95 and it may be instable; Secondly, the planned excavation scheme can sufficiently restrain the yield zones of the slope excavated, however, it barely inflected the top slope unexcavated. The result of this paper provides a reference for the actual project.