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A novel nanocavity-based polymer-on-insulator (POI) electro-optic modulator (EOM) is proposed. It consists of a polymeric photonic-crystal nanobeam cavity (PCNC) with ultra-low index-contrast (n_cavity/n_bg = 1.17). Based on three-dimensional (3D) finite-difference time-domain (FDTD) method, the PCNC design and optimization are investigated theoretically. A high quality-factor (Q) of 3.4 × 10⁴ and small mode-volume of 22.8 (λ/n_SEO)³ can be achieved. In order to judge the efficiency of the cavity design for electro-optic (EO) modulation, the optical modes and the electric field distribution are computed using an electromagnetic finite-element solver. Benefiting from the fast and strong EO effect in polymers, the modulator shows an EO modulation efficiency of up to 16 pm/V, which is over an order of magnitude higher than that in lithium niobate (LN) PCNCs. Moreover, the device is only 80 μm in length, leading to a voltage-length product V_π × L = 0.05 V·cm, which is much smaller than those of Mach-Zehnder modulators. To the best of our knowledge, this is the first on-chip POI-based EOM that features both ultra-compact size and high modulation efficiency. Hence, it is potentially an ideal platform for applications in optical communications, electric-field sensing, and tunable photonic circuits.