In this study, a high-efficiency single-pulsed femtosecond laser assisted with chemical wet etching method has been proposed to obtain large-area concave microlens array (MLA). The quasi-periodic MLA consisting of about two million microlenses with tunable diameter and sag height by adjusting laser scanning speed and etching time is uniformly manufactured on fused silica and sapphire within 30 minutes. Moreover, the fabricated MLA behaves excellent optical focusing and imaging performance, which could be used to sense the change of the liquid refractive index (RI). In addition, it is demonstrated that small period and high RI of MLA could acquire high sensitivity and broad dynamic measurement range, respectively. Furthermore, the theoretical diffraction efficiency is calculated by the finite domain time difference (FDTD) method, which is in good agreement with the experimental results.