Coherent fading has been regarded as a critical issue in phase-sensitive optical frequency domain reflectometry (φ-OFDR) based distributed fiber-optic sensing. Here, we report on an approach for fading noise suppression in φ-OFDR with multi-core fiber. By exploiting the independent nature of the randomness in the distribution of reflective index in each of the cores, the drastic phase fluctuations due to the fading phenomina can be effectively alleviated by applying weighted vectorial averaging for the Rayleigh backscattering traces from each of the cores with distinct fading distributions. With the consistent linear response with respect to external excitation of interest for each of the cores, demonstration for the propsoed φ-OFDR with a commercial seven-core fiber has achieved highly sensitive quantitative distributed vibration sensing with about 2.2 nm length precision and 2 cm sensing resolution along the 500 m fiber, corresponding to a range resolution factor as high as about about 4E-5. Featuring long distance, high sensitivity, high resolution, and fading robustness, this approach has shown promising potentials in various sensing techniques for a wide range of practical scenarios.