Physical Unclonable Functions (PUFs) are significant in building lightweight Internet of Things (IoT) authentication protocols. However, PUFs are susceptible to attacks such as Machine-Learning(ML) modeling and statistical attacks. Researchers have conducted extensive research on the security of PUFs; however, existing PUFs do not always possess good statistical characteristics and few of them can achieve a balance between security and reliability. This article proposes a strong response-feedback PUF based on the Linear Feedback Shift Register (LFSR) and the Arbiter PUF (APUF). This structure not only resists existing ML modeling attacks but also exhibits good Strict Avalanche Criterion (SAC) and Generalized Strict Avalanche Criterion (GSAC). Additionally, we introduce a Two-Level Reliability Improvement (TLRI) method that achieves 95% reliability with less than 35% of the voting times and single-response generation cycles compared to the traditional pure majority voting method.