Controlling the optical coupling between a micro-resonator and waveguide plays a key role in on-chip photonic circuits. Here, we demonstrate a two-point coupled lithium niobate (LN) racetrack micro-resonator that enables us to electro-optically traverse a full set of the zero-, under-, critical-, and over-coupling regimes with minimized disturbance of the intrinsic properties of the resonant mode. The modulation between the zero- and critical-coupling conditions cost a resonant frequency shift of only ∼344.2 MHz and rarely changed the intrinsic quality (Q) factor of 4.6 × 105. Our device is a promising element in on-chip coherent photon storage/retrieval and its applications.