In order to improve the spectral efficiency of the system and increase the transmission reliability, it is necessary to establish a spatial fading channel model to analyze the performance of massive Multiple-Input and Multiple-Output (MIMO) systems. Assuming that the elevation and azimuth angles follow the Laplacian distribution and the Von-Mises distribution, the analytical expressions of the spatial correlation coefficients between the elements of the uniform planar array antenna are derived. The MIMO multi-antenna system model is established to analyze the system performance. The effects of different angle spread in elevation power spectrum on the fading correlation and channel capacity of uniform planar arrays, and the effects of different signal-to-noise ratios and antenna array elements on spectral efficiency are studied. Compared with the traditional uniform linear array, the analysis results show that the uniform planar array is more suitable for the massive MIMO system than the uniform linear array in the millimeter wave scene, which makes it possible for the future mobile network to work in different frequency bands and cells.