In this paper, we report the time dependence of the magnetic field inside a YBa2Cu3O7 tube, when switching on a field He outside the tube after a zero field cooling the tube into a superconducting state. In our experiment He is smaller than 4Hrm, where Hrm is the trapped field of the tube. The dependence can be expressed as Hi(t)=H0 + B0(Int + 1-exp(-t/τ)), where H0, B0 and 1/τ are functions of He, and they keep rising when He>Hrm. We suggest that the term of Int is caused by flux lines creeping, while (1-exp(-t/τ)) results from flux lines fluctuating, which is a short time effect. The shielding effect of YBa2Cu3O7 tubes is perfect for low dc field (rm/2), and better than the best normal metal for ac magnetic noise.