We introduce Capacitive Micromachined Optical Focusing (CMOF) MEMS consisting of a miniature circular mirrored-membrane which can be electrostatically actuated to change mirror curvature. The central deflection zone is a close approximation to a parabolic mirror. The device is fabricated with minimal membrane mass to be only slightly larger than a diffraction-limited focus of a Gaussian beam. This device is a good candidate for fast tuning of the radius of curvature of laser beams at greater than MHz tuning rates, a feat difficult to achieve with current technologies. We present the design, modeling, and fabrication of a high-speed focusing CMOF MEMS platform. We have developed an equivalent circuit model for CMOFs which is capable of full nonlinear analyze of the CMOFs, and it is validated by ANSYS finite element method (FEM) simulations. By using the equivalent circuit model the non-linear transient response of a CMOF can be rapidly obtained and controlled with nonlinear control systems. The first generation of the proposed device is fabricated with a sacrificial-release process. Fabricated CMOFs have a silicon nitride membrane with 32um radius and 300nm gap spacing between top and bottom electrode. These CMOFs can effectively change their focal length from infinity to 3mm. We tested the device in an optical lens-assembly, and recorded 1mm focal point change by only 100nm deflection on the CMOF surface as measured using a Shack-Hartman wavefront sensor.