This study focuses on fabricating efficient CdS/CdTe thin-film solar cells with thermally evaporated cuprous iodide (CuI) as hole-transporting material (HTM) by replacing Cu back contact in conventional CdS/CdTe solar cells to avoid Cu diffusion. In this study, a simple thermal evaporation method was used for the CuI deposition. The current-voltage characteristic of devices with CuI films of thickness 5 nm to 30 nm was examined under illuminations of 100 mW/cm² (1 sun) with an Air Mass (AM) of 1.5 filter. A CdS/CdTe solar cell device with thermally evaporated CuI/Au showed power conversion efficiency (PCE) of 6.92% with J_SC, V_OC, and FF of 21.98 mA/cm², 0.64 V, and 0.49 under optimized fabrication conditions. Moreover, stability studies show that fabricated CdS/CdTe thin-film solar cells with CuI hole-transporters have better stability than CdS/CdTe thin-film solar cells with Cu/Au back contacts. The significant increase in FF and, hence, PCE, and the stability of CdS/CdTe solar cells with CuI, reveals that Cu diffusion could be avoided by replacing Cu with CuI, which provides good band alignment with CdTe, as confirmed by XPS. Such an electronic band structure alignment allows smooth hole transport from CdTe to CuI, which acts as an electron reflector. Hence, CuI is a promising alternative stable hole-transporter for CdS/CdTe thin-film solar cells that increases the PCE and stability.