The propagation properties of a hollow Gaussian beam (HGB) carrying on‐axis and off‐axis vortices through a high numerical aperture lens are investigated. The intensity of the focused beam in the focal plane can be controlled by choosing the different topological charges, the beam order, and the semi‐aperture angle. As intrinsic properties, vortex beams possess both spin and orbital angular momenta. The spin angular momenta (SAM) density can be treated as a vector in 3D since it exists in arbitrary orientation during the beam propagation. The vectors of SAM density orientation of the focused beam in 3D rotate around the central axis whose locations mainly rely on the vortices. The magnitude of the SAM density near the focus plane abruptly varies by altering the focal length of the lens. Under tightly focusing condition, two new pairs of vortices generate alternately on x and y axes in the vectorial electric fields, while the topological charges increase by one. Propagation properties of a hollow Gaussian beam carrying on‐axis and off‐axis vortices through a high numerical aperture lens are investigated. The magnitude of the spin density near the focus abruptly varies by altering the focal length of the lens. Additionally, two new pairs of vortices generate alternately in the vectorial electric fields while the topological charges increase by one.