This thesis investigates the performance of a phased array of antenna elements conforming to a paraboloidal surface. We hypothesize that such a conformal phased array would have performance comparable to that of a correspondingly sized planar array. The performance of a paraboloidal array of antenna elements was simulated using an array program, and the resulting gains, side-lobe levels, and half-power beamwidths compared to those of a similarly sized planar array. Furthermore, we propose a beam-forming feed network for this paraboloidal phased array, and discuss the influence that coupling between the elements could have on the array performance. Lastly, we propose that such an array be used in conjunction with a parabolic reflector antenna to form a versatile hybrid antenna with several potential applications.