Primary bronchus cancer is one kind of lung cancer with a very high mortality rate. Magnetic drug targeting (MDT) technology could concentrate drugs in a specific area, which could have useful application in lung cancer therapy. Due to a bulk superconducting magnet's ability to generate a superior magnetic field strength and gradient in comparison to conventional permanent magnets, there is great potential for achieving MDT external to the body. However, current research in this area is still in its infancy, and numerical simulations exploring the guidance ability of this technology have been limited to only two-dimensional geometries, which limits further exploration toward clinical transformation. In this work, a three-dimensional lung and bulk superconducting magnet model have been built in the finite-element software package COMSOL Multiphysics. The model is used to simulate the drug delivery process in the lung via the superconducting magnet. The influence of various parameters on the capture efficiency is investigated, including lung-magnet distance, bulk superconductor properties, particle properties, and physiological or tumor structural parameters. The results demonstrate that the bulk superconducting magnet can effectively improve the capture efficiency of magnetic drugs or drug carriers within a suitable distance outside of the body, which could potentially guide the design of a practical, external superconducting MDT system in the near future.