A cycloid-like variable curvature mirror (VCM) for zoom-imaging systems was investigated. An analytical-deformation solution to a thin-elastic plate with a cycloid-like thickness distribution and simply supported boundary condition under uniform pressure was found using a small parameter method. The finite-element analysis of the thin-elastic plate and designed VCM showed a good correlation with the analytical solution. The VCM was manufactured and polished to the initial shape with a root mean square (RMS) of 1/80λ. Finally, with air-pressure-based actuation testing under 0.07 MPa, the VCM deforms approximately 36.89 µm and maintains the RMS surface performance of 1/10λ, 1/40λ with and without spherical aberrations, respectively. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.