FFT-based digital spectral analyzer has become more and more widely used as a result of the development of Digital Signal Processing (DSP) techniques. Modern Analog-to-Digital Converters (ADC) and processors have made it possible to make fast measurements with a limited number of hardware.   In this thesis, a design of a simple low-cost FFT-based digital spectrum analyzer was presented. The author discusses the design of each components of the system in qualitatively and quantitatively. The report presents the whole system design in detail which contains filter design, micro-controller design, UART transmission design and MATLAB GUI design. Some satisfying measurement result of the system were presented in the paper. The system can provide fast measurement with good accuracy. But the measured result has a limited range and resolution of the display is not very high. At last, the advantages and disadvantages of the system was discussed which is considered as guidelines for further work.