We present observations of the Vela X region at 31 GHz using the Cosmic Background Imager (CBI). We find a strong compact radio source (5farcm9 × 4farcm1, 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' resolution for a 45' 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 α (Fν vprop να) of the PWN is flat, or even marginally positive, with a value of αimg1.gif = 0.10 ± 0.06, while the Vela X filamentary structure has a negative spectral index of αimg1.gif = -0.28 ± 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'' ± 20'' southwest 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.