We propose a new method to generate the carrier-envelope phase stable, > 200 µJ, ~ 1.1-cycle laser pulses at 2 µm wavelength, based on an optical parametric amplifier with the optimized angular dispersion. The angularly dispersed non-collinear angle is optimized over the entire bandwidth from 1.3 to 4 µm through the combination of a prism and a designed chirped grating. The phase mismatch is minimized over ~ 1.4 octave bandwidth, supporting the direct amplification of single-cycle pulses. The angularly dispersed signal is amplified to > 200 µJ pulse energy with the freedom of further energy scaling up through a single-stage optical parametric amplifier with a single bulk crystal. By implementing a symmetric 4-f system, the introduced angular and temporal dispersion of the amplified pulses is fully compensated to generate single-cycle pulses. The proposed parametric amplifier with the optimized angular dispersion provides a simple method to generate the high-energy, single-cycle pulses without constrains on nonlinear crystals, amplification wavelengths, pump sources, and compressors.