A novel microfiber sensor is proposed and demonstrated based on a singlemode-tapered hollow core-singlemode (STHS) fiber structure. Experimentally a STHS with taper waist diameter of $26.5~\mu \text{m}$ has been fabricated and RI sensitivity of 816, 1601.86, and 4775.5 nm/RIU has been achieved with RI ranges from 1.3335 to 1.3395, from 1.369 to 1.378, and from 1.409 to 1.4175 respectively, which agrees very well with simulated RI sensitivity of 885, 1517, and 4540 nm/RIU at RI ranges from 1.3335 to 1.337, from 1.37 to 1.374, and from 1.41 to 1.414. The taper waist diameter has impact on both temperature and strain sensitivity of the sensor structure: (1) the smaller the waist diameter, the higher the temperature sensitivity, and experimentally 26.82 pm/°C has been achieved with a taper waist diameter of $21.4~\mu \text{m}$ ; (2) as waist diameter decrease, strain sensitivity increase and 7.62 pm/ $\mu \varepsilon $ has been achieved with a taper waist diameter of $20.3~\mu \text{m}$ . The developed sensor was then functionalized for human chorionic gonadotropin (hCG) detection as an example for biosensing application. Experimentally for hCG concentration of 5 mIU/ml, the sensor has 0.5 nm wavelength shift, equivalent to limit of detection (LOD) of 0.6 mIU/ml by defining 3 times of the wavelength variation (0.06 nm) as measurement limit. The biosensor demonstrated relatively good reproducibility and specificity, which has potential for real medical diagnostics and other applications.