Integrated optical power splitters are basic but indispensable on-chip devices in silicon photonics. They can be used either for power distribution or monitoring, or as the building blocks for more complex devices or circuits. Although different types of optical power splitters with different architectures have been proposed and demonstrated, devices that could work with arbitrary power splitting ratio in a large bandwidth without polarization dependence are still rare to be seen. In this paper, we propose and investigate an optical power splitter with adiabatically tapered waveguide structures on a thick silicon nitride platform, which could meet the requirement mentioned above. With optimized structural parameters obtained by three-dimensional finite-difference time-domain (3D-FDTD) simulation, the polarization dependence of different power splitting ratio gets almost eliminated for each specific working wavelength. In a broad wavelength range (1 340—1 800 nm), the insertion loss (IL) of the device is below 1 dB, and the variation of the power splitting ratio (PSR) can be controlled within ~±5% if compared with the targeted design value for 1 550 nm centered wavelength. Simple structure, relaxed critical dimensions, and good fabrication tolerance make this device compatible with the standard fabrication process in commercial silicon photonic foundries.