We utilized the splitoperator method to numerically solve the onedimensional GrossPitaevskii equation. The quantum tunneling time was defined as the time difference corresponding to the maximum value of the modulus square of the wave function when entering and exiting the barrier. We obtain the tunneling time and tunneling probability of its bright soliton solution through a Gaussian potential barrier of a certain width at different energies. It was observed that when the incident energy is less than the barrier height，the tunneling time increases with the incident energy. When the incident energy is greater than the barrier height，the tunneling time is inversely proportional to the tunneling velocity. Furthermore，within different energy ranges，the effects of the oscillation frequency of the barrier on the quantum tunneling time and probability were studied when the barrier undergoes smallamplitude oscillations. It is observed that under the quantum state with incident energy less than the barrier height，different barrier oscillation frequencies caused significant oscillations in the tunneling time.