Recently, it has been reported that small-scale (&lgr;~0.1--2 km) density irregularities occur during 100-Hz electric field bursts in the nightside ionosphere of Venus. The correlation of field and plasma fluctuations suggests that a local plasma instability may be responsible for the turbulence. In this paper we provide a detailed analysis of the lower-hybrid-drift instability as a mechanism to generate the observed irregularities. We develop a fully electromagnetic theory that is relevant to the finite &bgr; plasma in Venus' ionosphere and include collisional effect (e.g., electron-ion electron-neutral, and ion-neutral collisions). The key features of the analysis that favor this instability are (1) it is a flute mode and propagates orthogonal to the ambient magnetic field, (2) it is a relatively short wavelength mode and the Doppler-shifted frequency can be >100 Hz, (3) it can produce both electric field and density fluctuations, as well as magnetic field fluctuations in a finite &bgr; plasma, and (4) it is most unstable in low-&bgr; plasma (i.e., &bgr;≲1) so that it is likely to occur in the low-density, high-magnetic-field ionospheric holes. These features are consistent with observational results.