In classical supergiant X-ray binaries (SgXBs), the Bondi-Hoyle-Lyttleton wind accretion was usually assumed, and the angular momentum transport to the accretors is inefficient. The observed spin-up/spin-down behavior of the neutron star in SgXBs is not well understood. In this paper, we report an extended low state of Vela X-1 (at orbital phases 0.16-0.2), lasting for at least 30 ks, observed with Chandra during the onset of an unusual spin-up period. During this low state, the continuum fluxes dropped by a factor of 10 compared to the preceding flare period, and the continuum pulsation almost disappeared. Meanwhile, the Fe Kα fluxes of the low state were similar to the preceding flare period, leading to an Fe Kα equivalent width (EW) of 0.6 keV, as high as the Fe Kα EW during the eclipse phase of Vela X-1. Both the pulsation cessation and the high Fe Kα EW indicate an axisymmetric structure with a column density larger than 10 24 cm −2 on a spatial scale of the accretion radius of Vela X-1. These phenomena are consistent with the existence of an accretion disk that leads to the following spin-up of Vela X-1. It indicates that disk accretion, although not always, does occur in classical wind-fed SgXBs.