This paper investigates the tight focusing properties of the partially coherent radially polarized rotationally-symmetric power-exponent-phase vortex (RPEPV) beam, namely, the radially polarized multi-Gaussian Schell-model RPEPV beam. Specifically, a theoretical model of the partially coherent radially polarized RPEPV beam is built. The Richards-Wolf vectorial diffraction integral theory is applied to study the tight focusing model of the partially coherent radially polarized RPEPV beam passing through a high numerical aperture objective, and the cross-spectral density function of the beam at the focal plane is deduced. Then, the distribution characteristics of the spot intensity, coherence degree, and polarization degree of the focused field are numerically analyzed. The research results show that the parameters, such as beam order, topological charge, power exponent, and coherence width, can be changed to obtain various focal spot distributions, including Gaussian, flat-topped, and polygonal distributions.