We propose an effective scheme based on redundant residue number systems (RRNS) for radiation hardening of datapath in this paper. The proposed hardening scheme employs redundant residues to mitigate soft errors. We use the properties of RRNS, such as independence, parallel and error correction, to establish the radiation hardening architecture for datapath in radiation environments. In the architecture, all of the residues can be processed independently, and most of soft errors in datapath can be corrected with the redundant relationship of the residues at correction module, which is allocated at the end of the architecture. There is not any additional processing in the architecture but correction operation and binary to residue translation. Thus, the proposed scheme has high efficiency when the processing steps of datapath are large. In order to provide protection for the key module in the proposed scheme, correction module, some traditional protection methods, including Guard-gate register triple modular redundancy (G-RTMR), pipeline-level TMR, and module-level TMR, are used to construct the hybrid protection schemes. In the case studies, we find that the RRNS based scheme and the hybrid schemes can reduce soft error rate from 10-12 to 10-17, -18,10-25, and -25-respectively, only with 45.-46.1% area overheads and negligible latency overheads, when the pipeline stages of datapath are 104 and the moduli set with correction capability of one residue is adopted. The case studies also show that the proposed schemes can achieve less area and latency overheads than that of datapath without radiation hardening, because RRNS can reduce the complexity of operations in datapath. [ABSTRACT FROM AUTHOR]