Magnetic random-access memory (MRAM) suffers from reliability issues subject to the harsh industrial environment and applications with limited hardware resources. Thus, we propose the new spin-orbit torque MRAM (SOT-MRAM) scheme called exchange bias (EB) MRAM for error-tolerant application. EB MRAM enhances reliability from its immunity to external magnetic and higher endurance. In addition, this paper presents near-memory computing (NMC) with EB MRAM to further achieve low soft error sensitivity and latency implementation. In the proposed scheme, the NMC controller exploits the accelerated design to reduce data movement, and EB MRAM as the computation memory is performed with subword-level compression. The experimental results show that the access time and energy of EB MRAM is only 0.9ns and 0.113pJ/bit while the data compressed rate is up to 75% with 2.05% loss over the state-of-the-art designs.