Gesture air-writing is an advanced nontouching interaction method that replaces traditional typewriter keyboards, touch screens and other input devices. Due to its low power consumption, noncontact detection and independence from light conditions, millimeter wave radar has become a valuable gesture air-writing solution. In this paper, we proposed a prototype of a gesture air-writing tracking system that is based on the 24-GHz frequency-modulated continuous-wave (FMCW) radar system-on-chip (SoC). The transmitted chirp signal of this radar chip covers up to a 4-GHz bandwidth, which provides sufficient range resolution to track hand gestures. With the development of single input, multiple output (SIMO) antennas, the air-writing symbols can be reconstructed in an observation plane. A system design and signal processing algorithm for gesture air-writing applications is proposed for the prototype system in this paper. To test the performance of the proposed method, experiments with cases of five simple gestures, air-writing numbers and letter tracking are carried out. The experimental results verify the efficiency and accuracy of the proposed method.