Millimeter wave (mm-wave) communication is widely considered to be a promising technique for 5G (Fifth Generation) cellular systems. Owing to the high path loss of mm-wave channels, 5G networks could employ a heterogeneous structure that consists of an MBS (Macro Base Station) and numerous SBSs (Small Base Stations). In this paper, we analyze the coverage and rate performance of an mm-wave heterogeneous network. Using user beam selection, we derive analytical expressions for the coverage probabilities of the SBSs and MBS. Furthermore, the average achievable rate for a typical user is also investigated. It is shown that the analytical results closely follow those of the simulations with marginal differences.