A birefringent-refraction (BR) sensor for measuring refractive indices of liquid solutions based on phase interrogation in a heterodyne interferometer is proposed. In comparison with the TIR and SPR sensors, the sensitivity of the proposed BR sensor is less dependent on the specific incident angles (critical and resonance angle). A measurement resolution of 3 × 10−6 RIU is achievable in the RI range of 1.4 × 10−2 RIU.