A domain with C^2 boundary in complex space is called pseudoconvex if it has a C^2 defining function with positive complex hessian on its boundary. Pseudoconvexity is a generalization of convexity. It can be realised as a domain with geometric condition on the boundary and its topology can be studied by Morse theory. In this talk, we will discuss the Morse index theorem for free boundary minimal disks for partial energy in strictly pseudoconvex domain and the relation between holomorphicity and stability of the free boundary minimal disk. We will also give an example to illustrate the necessity of strict pseudoconvexity in our index estimate.