This paper analyzes the capacity of the finite scatterer (FS) multiple-input multiple-output (MIMO) channel model with finite angular resolution. The rank of the channel is bounded by not only the number of antennas but also the finite angular resolution of antenna arrays. The probability mass function (PMF) of rank is studied and derived based on the Stirling number of the second kind. As a result, the closed-form expression of the capacity of a FS MIMO channel model is obtained. Furthermore, asymptotic analyses such as the large-scale system analysis, infinite scatterer analysis, and the multiplexing gain analysis are investigated.