Line jittering, or random horizontal displacement in video images, occurs when the synchronization signals are corrupted in video storage media, or by electromagnetic interference in wireless video transmission. The goal of intrinsic video dejittering is to recover the ideal video directly from the observed jittered and often noisy frames. The existing approaches in the literature are mostly based on local or semi-local filtering techniques and autoregressive image models, and complemented by various image processing tools. In this paper, based on the statistical rationale of Bayesian inference, we propose the first variational dejittering model based on the bounded variation (BV) image model, which is global, clean and self-contained, and intrinsically combines dejittering with denoising. The mathematical properties of the model are studied based on the direct method in Calculus of Variations. We design one effective algorithm and present its computational implementation based on techniques from numerical partial differential equations (PDE) and nonlinear optimizations.