Along with the National Institute of Standards and Technology (NIST) post-quantum cryptography (PQC) standardization process, lightweight PQC-related research and development have also gained substantial attention from the research community recently. Ring-Binary-Learning-with-Errors (RBLWE), a lightweight variant of Ring-LWE, which uses binary errors to replace the regular Gaussian distributed errors to achieve smaller complexity, has great potential to built such lightweight PQC scheme for emerging Internet-of-Things (IoT) and edge computing applications.The parameter settings of the RBLWE-based encryption scheme, however, are much smaller than the typical Ring-LWE one and then how to reduce its computational complexity becomes an interesting research topic.Following this direction, in this paper, we propose a Karatsuba Initiated Novel Accelerator (KINA) for efficient implementation of RBLWE-based PQC. Overall, we have made several coherent interdependent stages of efforts to carry out the proposed work: (i) we have presented the mathematical derivation process to propose a new Karatsuba Algorithm (KA)-based  polynomial multiplication, the main algorithmic operation of the RBLWE-based scheme; (ii) we have then effectively mapped the proposed algorithm into a desired hardware accelerator with the help of a number of optimization techniques; (iv) we have also provided detailed complexity analysis and implementation comparison to demonstrate the superior performance of the proposed RBLWE-based PQC accelerator. Overall, the proposed RBLWE-based PQC accelerator involves two unique features: (i) this is the first report about Karatsuba initiated RBLWE-based PQC accelerator; (ii) the proposed RBLWE-based PQC accelerator offers flexible processing speed and can be fit in various high-performance applications. The proposed KINA is highly efficient and has the potential to be included in the implementation recommendation choices for RBLWE-based scheme deploying in lightweight applications.