Classical designs of optical transimpedance preamplifier for p-i-n photodiode receiver circuits generally employ common source transimpedance input stages. In this paper, we explore the design of a class of current-mode optical transimpedance preamplifier based upon common gate input stages. A feature of current-mode optical transimpedance preamplifier is high gain and high bandwidth. The bandwidth of the transimpedance preamplifier can also be increased by the capacitive peaking technique. In this paper we included the development and application of a circuit analysis technique based on the minimum noise. We develop a general formulation of the technique, illustrate its use on a number of circuit examples, and apply it to the design and optimization of the low-noise transimpedance amplifier. Using the noise minimization method and the capacitive peaking technique we designed a transimpedance preamplifier with low noise, high-speed current-mode transimpedance preamplifier with a 1.57GHz bandwidth, and a 2.34K transimpedance gain, a 470nA input noise current. The proposed preamplifier consumes 16.84mW from a 3.3V power supply.