Few-cycle short-wave infrared (SWIR) pulses are useful tools for research on strong-field physics and nonlinear optics. Here we demonstrate the amplification of sub-cycle pulses in the SWIR region by using a cascaded BBO-based optical parametric amplifier (OPA) chain. By virtue of the tailored wavelength of the pump pulse of 708 nm, we successfully obtained a gain bandwidth of more than one octave for a BBO crystal. The division and synthesis of the spectral components of the pulse in a Mach-Zehnder-type interferometer set in front of the final amplifier enabled us to control the dispersion of each spectral component using an acousto-optic programmable dispersive filter inserted in each arm of the interferometer. As a result, we successfully generated 0.73-optical-cycle pulses at 1.8 μm with a pulse energy of 32 μJ.