The object of study is the geodesic structure of a Lifshitz black hole in 3+1 space-time dimensions, which is an exact solution to the Einstein-scalar-Maxwell theory. The motion of massless and massive particles in this background is researched using the standard Lagrangian procedure. Analytical expressions are obtained for radial and angular motions of the test particles, where the polar trajectories are given in terms of the -Weierstra elliptic function. It will be demonstrated that an external observer can see that photons with radial motion arrive at spatial infinity in a finite coordinate time. For particles with non-vanished angular momentum, the motion is studied on the invariant plane and, it is shown that bounded orbits are not allowed for this space-time on this plane. These results are consistent with other recent studies on Lifshitz black holes.