Bio-inspired flapping hydrofoils can be used for propulsion or energy extraction, which has aroused the interest of many scholars. This paper experimentally and numerically studies the propulsion of semi-active hydrofoils used for wave glider. For NACA 0012 foil section, heave amplitude h0 = 1.0 chord, Reynolds number Re=2×104, a series of experiments were conducted. We investigate the effects of the dimensionless torsion stiffness K* = 0.55, 0.77, 1.69, and 2.30 on the semi-active flapping propulsion performance, and the pivot location factors are also considered. Unlike the fully-active flapping, which is often configured with pivot location 1/3c, the results suggest that for the pivot location xp=0.33c, the pitch angle is small at a mid and low oscillating frequency, and the semi-active flapping foil is in an almost pure heave state, which leads to low efficiency, even if weak stiffness is selected. Under the conditions of stiffness K* = 1.69 and pivot location xp = 0.09c, the propulsion efficiency can be increased to over 40%. For the wave glider, the pivot location xp = 0.16c with non-dimensional stiffness K*=1.69 configuration is recommended because it has a larger propulsion coefficient and a not bad efficiency.