Quantum key distribution (QKD) offers unconditional security for remote communication based on the fundamental principles of quantum mechanics. However, existing QKD with correlated sources protocols suffer from limited tolerance to source correlation, which significantly degrades the key generation rate and restricts the secure transmission distance, thereby limiting their practical deployment. In this work, we propose an improved QKD with correlated sources protocol that overcomes these limitations by discarding the traditional loss-tolerant security framework. Instead, our approach adopts the standard BB84 protocol for the security analysis, under the assumption that the source correlation has a bounded range and characterized inner product of the states. We theoretically analyze the performance of the improved protocol under various levels of source correlation and channel loss. Numerical simulations show that our protocol achieves a significantly higher secret key rate and longer transmission distance compared to conventional schemes. Under typical parameters and in the case of 0 dB loss, our protocol achieves approximately a 1.5 to 3 fold improvement in secret key rate. Additionally, the maximum tolerable loss is enhanced by approximately 2 to 6 dB. This highlights a promising direction for enhancing the robustness and practicality of QKD with correlated sources systems, paving the way for their deployment in real-world quantum communication networks.