In this paper, we prove common fixed-point theorems in complete b-metric spaces using rational type contraction for two self-mappings. Our result improves and extends the results proved by Mlaiki et al. [1] for a single continuous self-mapping in extended complete b- metric space. We improve the results of Mlaiki et al. [1] to complete b-metric spaces for two self-mappings without assuming the continuity of any mapping.