We propose and demonstrate broadband focusing grating couplers for suspended-membrane waveguides on silicon-on-insulator both in near-infrared (near-IR) and in mid-IR wavelength range. Finite-difference time-domain simulation predicts ∼100 nm 3 dB bandwidth with -1.7 dB coupling efficiency for an apodized grating in near-IR. -3.5 dB maximum coupling efficiency and ∼90 nm 3 dB bandwidth are realized experimentally. In mid-IR, -5.5 dB maximum coupling efficiency from a uniform focusing grating is measured at 2.75 μm, and ∼500 nm 3 dB bandwidth is predicted theoretically.