Superconducting nanowires single-photon detectors (SNSPDs or SSPDs) have emerged as an attractive single-photon detection technology with high performance. Two types of SNSPDs have been developed so far. One is the standard-fiber-coupled SNSPD with the light normally incident on the meandered nanowires, the other is waveguide-coupled SNSPD with the nanowires fabricated on the surface of the waveguide which guides photons while the fiber is coupled to the waveguide. Here we propose a new type of SNSPD integrated with microfiber. The photons are guided by a microfiber and evanescently absorbed by the nanowire of SNSPD when the nanowire is parallel and very close to the microfiber. The numerical simulation results show that the fiber to detector coupling efficiency can be close to unity with optimized device structure/parameters. With a minimal total NbN nanowire length of about 300 μ m, the absorption of the nanowire can reach 90%.