In this paper, we have studied the shielding properties of a high temperature superconducting (HTS) bulk tube-shaped cylinder in varying magnetic fields. Within this scope, we have simulated the hollow cylinder geometry in axis-symmetric finite element method (FEM) in which the electromagnetic properties of a HTS are described by a nonlinear electric field-current density (E - J) power law including a critical current density depending on magnetic field. In the first stage, we have analyzed temperature dependence of shielding factor (SF), which is described as the ratio of the applied magnetic field to the magnetic field in the center of the hollow cylinder. In the second stage, the effect of magnetic field's sweep rate (dB(app)/dt) on the magnetic shielding was numerically examined. In the final stage, using the certain lines over the superconducting tube, we have worked out the shielding field (B-sz) of the HTS tube by subtracting the z-component of magnetic field (B-z) from applied magnetic field (B-app). Our numerical investigations indicate that the superconducting tube can provide field and temperature-controlled magnetic shielding.