A three-dimensional reconstruction of the 2002 April 21 partial halo Coronal Mass Ejection (CME) has been made based on the O VI 1032 A and [Fe XVIII] 974 A lines observed by the Ultraviolet Coronagraph Spectrometer (UVCS) on board the Solar and Heliospheric Observatory (SOHO). We use the Doppler velocities to derive the CME structure along the line of sight. UVCS observed the O VI line profiles split into strongly Doppler red- and blueshifted components, and the region of split profiles grew rapidly along the long spectrograph slit. The more localized [Fe XVIII] bright emission starts at the same time as the maximum Doppler redshift of O VI, indicating that it is inside the CME. In the view from the solar west, the O VI looks like halo CMEs seen by the Large Angle and Spectrometric Coronagraph (LASCO). The [Fe XVIII] bright emission appears as a barlike structure seen nearly end-on from the Earth, and side-on from the solar north and from solar west. The reconstructed [Fe XVIII] emission allows two interpretations, as ejection of preexisting hot plasma or as a current sheet. The evidence favors the current sheet interpretation, although we cannot rule out the alternatives.