We present the spatially resolved optical spectroscopy of the (12 arcsec x 24 arcsec) Crab-pulsar neighbourhood in the range 4600-5700 A made with the Multipupil Fiber Spectrograph at the 6m telescope of the SAO RAS. The spectra exhibit blue- and red-shifted strong [OIII] and weaker H_beta and HeII emission lines with the shifts and intensities varying with the position in the field by a certain way. They hint the presence of a cylindrical, cone-like, rotating structure centered at the pulsar position and oriented along the symmetry axis of the compact, torus-like pulsar nebula seen in optical continuum and soft X-rays. The structure is likely associated with the pulsar nebula. In the case, the nebula rotates counter-clockwise with respect to its symmetry axis, or the pulsar spin axis, and the estimated rotational velocity at cylindrical radii of several thousand AU from the pulsar is ~ 2000-3000 km/s.

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