The recent realization of all-dielectric valley photonic crystals (VPCs) in nanoscale not only provides a standard platform to explore many topological phases of light with protected edge modes, but also shows promising applications for designing high-performance nanophotonic devices. However, the widely reported all-dielectric VPCs are limited to one single polarization, and it is challenging to manipulate the polarization degree of freedom of light and design polarizing devices using VPCs. Here, we design a dual-polarization all-dielectric VPC and propose a topological polarization beam splitter. The phase vortex distributions of bulk modes at different valleys characterize the nonzero valley Chern numbers for both TE and TM polarizations, indicating the implementation of topologically nontrivial dual-polarization band gaps. This leads to dual-polarization valley-dependent edge modes located at interfaces with different shapes. The topological valley transport around sharp-bends is also demonstrated for both TE and TM polarizations. Finally, a harpoon-shaped polarization beam splitter is proposed, and the simulated results confirm the good functionality of polarization separation. Our work shows the flexible control of light in topological photonic systems with the polarization degree of freedom, and has promising applications in polarization multiplexing photonic devices owing to the enlarged the optical information-processing capacity.