Gigabit free-space transmissions are experimentally demonstrated with a quantum cascaded laser (QCL) emitting at mid-wavelength infrared of 4.65 μm, and a commercial infrared photovoltaic detector. The QCL operating at room temperature is directly modulated using on-off keying and, for the first time, to the best of our knowledge, four- and eight-level pulse amplitude modulations (PAM-4, PAM-8). By applying pre- and post-digital equalizations, we achieve up to 3 Gbit/s line data rate in all three modulation configurations with a bit error rate performance of below the 7% overhead hard decision forward error correction limit of 3.8×10-3. The proposed transmission link also shows a stable operational performance in the lab environment.