Since the analysis of cell coverage faces complex environments in unmanned aerial vehicle base station (UAV-BS) systems, general coverage probability in a typical cell is derived to analyse a UAV-BS multi-tier network, and this coverage probability is closely related with power difference among UAV-BSs, two-dimension (2D) and three-dimension (3D) UAV-BS deployment, and general interference fading models. Especially, closed-form coverage probability expressions are also derived in the form of 2D scenario and 3D scenario, when the interference fading coefficient is assumed to follow a Gamma distribution and an exponential distribution, respectively. It shows that there exists maximum spectral efficiency density (SED) as the BS density increases, and such a BS density achieving the max-SED is independent of noise power, but is affected by various propagation parameters.