A mid-infrared (mid-IR)-focusing subwavelength grating (SWG) coupler and suspended membrane waveguide (SMW) on a silicon-on-insulator wafer are studied. For a transverse-electric mode uniform SWG, finite-difference time-domain simulation predicts 44.2% coupling efficiency with 1 dB bandwidth of about 220 nm and backreflection of 0.78% at 2.75 μm. Then the uniform SWG is curved to a focusing SWG using a phase-matching formula. The SMWs are analyzed by the finite element method and fabricated. An Er3+-Pr3+ co-doped mid-IR fiber laser is used for device characterization. The fabricated mid-IR SWG coupler has 24.7% coupling efficiency.