A tunable optical delay line (ODL) featuring high switching speed and low optical loss is highly desirable in many fields. Here, based on the thin-film lithium niobate platform, we demonstrate a digitally tunable on-chip ODL that includes five Mach–Zehnder interferometer optical switches, four flip-chip photodetectors, and four delay-line waveguides. The proposed optical switches can achieve a switching speed of 13 ns and an extinction ratio of 34.9 dB. Using a modified Euler-bend-based spiral structure, the proposed delay-line waveguide can simultaneously achieve a small footprint and low optical propagation loss. The proposed ODL can provide a maximum delay time of 150 ps with a resolution of 10 ps and feature a maximum insertion loss of 3.4 dB.