Extreme-ultraviolet late phase (ELP) refers to the second extreme-ultraviolet (EUV) radiation enhancement observed in certain solar flares, which usually occurs tens of minutes to several hours after the peak of soft X-ray emission. The coronal loop system that hosts the ELP emission is often different from the main flaring arcade, and the enhanced EUV emission therein may imply an additional heating process. However, the origin of the ELP remains rather unclear. Here we present the analysis of a C1.4 flare that features such an ELP, which is also observed in microwave wavelengths by the Expanded Owens Valley Solar Array. Similar to the case of the ELP, we find a gradual microwave enhancement that occurs about 3 minutes after the main impulsive phase microwave peaks. Radio sources coincide with both foot points of the ELP loops and spectral fits on the time-varying microwave spectra demonstrate a clear deviation of the electron distribution from the Maxwellian case, which could result from injected nonthermal electrons or nonuniform heating to the footpoint plasma. We further point out that the delayed microwave enhancement suggests the presence of an additional heating process, which could be responsible for the evaporation of heated plasma that fills the ELP loops, producing the prolonged ELP emission.