An asymmetrical tapered singlemode–multimode–singlemode (SMS) fiber coupler based on two parallel physical contact SMS fiber structures was proposed. Since the coupler includes modes both from fiber core and cladding, two dips of the transmission spectrum exhibit different sensing characteristics to the surrounding temperature and refractive index (RI) change, which allows the use of the standard matrix inversion method to determine temperature and RI simultaneously. The temperature sensitivities of 0.0498 and 0.0324 nm/°C and RI sensitivities of 1151.76 and 1325.66 nm/RIU have been achieved, respectively. For biosensing application, with the functionalized fiber coupler sensor, a human chorionic gonadotropin concentration of 0.05 mIU/mL has been detected for a wavelength shift of 0.2 nm with good stability and excellent selectivity. The developed tapered SMS fiber coupler structure has advantages of simultaneous measurement of two independent parameters, simple configuration, low cost, and good repeatability that offer a great potential for medical diagnostics.