Studying geodesic variations and associated Jacobi vector fields is very useful for examining the theory of curvature in local and global Riemannian geometry. This is directly connected with the investigation of the geometry of small geodesic spheres and tubes, so it can be used in the analysis of the curvature of the ambient space. In this paper, the explicit expressions for the Jacobi vector fields on complex space forms will be used for calculating the matrix of the shape operator of tubes about geodesics on complex space forms.