Self-Powered neutron detectors (SPND) detect current generated from interaction of neutron flux with emitter materials. They are inside a reactor in NPP (Nuclear Power Plant), and currently used to monitor the output and control the operation. Since the signal level of prompt-response SPND is very small (-nA), an analog circuit is necessary to amplify the current signal, and to convert it into voltage. This circuit needs to perform an anti-aliasing function to reduce distortion at the stage of digital conversion. In this paper, a systematic design process for high-gain amplification circuit is presented. Based on error analysis of the circuit, parameters are selected to satisfy design requirements. A third-order anti-aliasing filter is designed. A prototype circuit is built. Measured performance of the circuit confirms that the circuit satisfies all design requirements and validates the efficacy of the design to be used in practical environments.