Thermal diodes, which allow heat transfer in a preferential direction while being blocked in a reverse direction, have numerous applications in thermal management, information processing, energy harvesting, etc. Typical materials of thermal diodes in previous works include phase-change and magneto-optical materials. However, such thermal diodes depend highly on specific working temperatures or external magnetic fields. In this work, we propose a near-field radiative thermal diode (NFRTD) based on two Weyl semimetal (WSM) nanoparticles (NPs) mediated by a WSM planar substrate, which works without an external magnetic field and with flexible temperatures. Numerical results show that the maximum rectification ratio of NFRTD can be up to 2673 when the emitter is 200 K and receiver is 180 K, which exceeds the maximum value reported in some previous works by more than 10 times. The underlying physical mechanism is the strong coupling of the localized plasmon modes in the NPs and nonreciprocal surface plasmon polaritons in the substrate. In addition, we calculate the distribution of the Green's function and reflection coefficient to investigate nonreciprocal energy transfer in NFRTDs. Finally, we discuss the effects of momentum separation on the rectification performance of the NFRTD. This work demonstrates the great potential of WSMs in thermal rectification and paves a path for designing high-performance NFRTDs.