We present observations of the Vela X region at 31 GHz using the Cosmic Background Imager ( CBI ) . We find a strong compact radio source ( 5.9 ^ { \prime } \times 4.1 ^ { \prime } , FWHM ) about the Vela pulsar , which we associate with the Vela pulsar wind nebula ( PWN ) recently discovered at lower radio-frequencies . The CBI ’ s 4 ^ { \prime } resolution for a 45 ^ { \prime } field of view allows the PWN to be studied in the large-scale context of Vela X. Filamentary structure in Vela X , which stands out in lower frequency maps , is very low-level at 31 GHz . By combining the 10 CBI channels , which cover 26-36 GHz , and 8.4 GHz archive data , we study the spectral energy distribution ( SED ) of the PWN and the brightest filaments . Our results show that the spectral index \alpha ( F _ { \nu } \propto \nu ^ { \alpha } ) of the PWN is flat , or even marginally positive , with a value of \alpha _ { 8.4 } ^ { 31 } = 0.10 \pm 0.06 , while the Vela X filamentary structure has a negative spectral index of \alpha _ { 8.4 } ^ { 31 } = -0.28 \pm 0.09 . The SED inhomogeneity observed in Vela X suggests different excitation processes between the PWN and the filaments . We investigate whether the PWN ’ s flat spectrum is a consequence of variability or truly reflects the SED of the object . We also investigate the nature of the Vela X filamentary structure . A faint filament crosses the PWN with its tangent sharing the same position angle as the PWN major axis , suggesting that it might be an extension of the PWN itself . The SED and bulk morphology of Vela X are similar to those of other well-studied plerions , suggesting that it might be powered by the pulsar . The peak of the PWN at 31 GHz is 80 ^ { \prime \prime } \pm 20 ^ { \prime \prime } south-west of the peak at 8.4 GHz . This shift is confirmed by comparing the 31 GHz CBI image with higher resolution 5 GHz Australia Telescope Compact Array observations , and is likely to be due to SED variations within the PWN .