In graphene-based optoelectronic devices, the ultraweak interaction between a light and monolayer graphene leads to low optical absorption and low responsivity for the photodetectors and relative high half-wave voltage for the phase modulator. Here, an integration of the monolayer graphene onto the side-polished optical fiber is demonstrated, which is capable of providing a cost-effective strategy to enhance the light–graphene interaction, allowing us to obtain a highly efficient optical absorption in graphene and achieve multifunctions: photodetection and optical phase modulation. As a photodetector, the device has ultrahigh responsivity ($1.5\times {10}^7\mathrm{A}/\mathrm{W}$) and high external quantum efficiency ($>1.2\times {10}^9\%$). Additionally, the polybutadiene/polymethyl methacrylate (PMMA) film on the graphene can render the device an optical phase modulator through the large thermo-optic effect of the PMMA. As a phase modulator, the device has a relatively low half-wave voltage of 3 V with a 16 dB extinction ratio in Mach–Zehnder interferometer configuration.