Using Dirac equation together with the Wigner distribution function, the trembling motion, known as Zitterbewegung effect, of moving electrons in quasi-one-dimensional relativistic quantum plasma is theoretically investigated. The relativistic Wigner matrix is used to calculate the mean values of the position and velocity operators for a Dirac gas of electrons. It is found that the oscillatory behavior of measurable quantities could be associated with the Zitterbewegung effect which manifests itself as a damping interference pattern stemming from mixing the positive and negative dispersion modes of Dirac particles.