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Three-dimensional numerical simulations are carried out to study the hydrodynamic performance and flow features of a bio-inspired underwater propulsor. The propulsor is constituted by a passive pitching panel. The leading edge of the panel is prescribed under a periodic heaving motion while the panel pitches passively due to the employing of a stiffness-lumped torsional spring at the leading edge. Effects of the torsional spring stiffness have been put emphases on. A real-time tunable stiffness strategy is presented and employed in the study. We first study the passive pitching effects on the hydrodynamics and flow features of the panel using a series of constant stiffness and then we study the tunable stiffness effects using cosinusoidal curve based waveforms, in which the effects of phase difference (ϕ) between the stiffness profile and the oscillation motion and as well as the effects of stiffness fluctuation amplitude (Gk) are investigated, respectively. The stiffness profile beneficial for propulsion efficiency is further applied to cases with different oscillation amplitudes. A high-fidelity immersed boundary method based direct numerical simulation (DNS) solver is employed to acquire the fluid dynamics and to simulate the flow. The panel passive pitching motion is solved by coupling the DNS flow solver and the Euler rigid body dynamic equation. Results show that for the constant stiffness cases, the panel generates sinusoidal-like pitching motion, and in certain stiffness range, flexibility could benefit efficiency while holding some extent of stiffness could enhance the thrust. For the tunable stiffness cases, it is found that both the mean thrust and propulsive efficiency improved when the stiffness change is in-phase with the heaving motion (ϕ = 0). The largest mean thrust is found at ϕ = 120 degree.