A metasurface is one of the most effectual platforms for the manipulation of complex optical fields. One of the current challenges in the field is to develop active or reconfigurable functionalities to extend its operation band which is limited by its intrinsic resonant nature. Here we demonstrate a kind of active Fano-resonant asymmetric metasurface in the near-infrared (NIR) region with heterostructures made of a layer of asymmetric split-ring resonators and a thin layer of phase-change material (PCM). In the asymmetric metasurface, significant tunability in the frequency, Q-factor and strength of the Fano resonance are all achieved by precisely controlling the phase transition of the contained PCM Ge2Sb2Te5 (GST), together with changing the geometric asymmetry of the split-ring resonators. Moreover, we provide a complete transition process of the optical properties for GST and an optimized modulation on the active Fano-resonant metasurface. Our approach to dynamically control a Fano-resonant metasurface paves the way to realizing various active photonic meta-devices involving PCM.