A novel two-electrode, frequency-scan electrical impedance tomography (EIT) system for gesture recognition not only reduces the measurement complexity and the number of electrodes, but also achieves a high accuracy in recognizing common gestures and pinch gestures. A bespoke circuit with two medical electrodes was developed to collect data from the back of the hand and presented a frequency-scan method to increase the diversity of impedance data. The data were processed using data cleaning and feature extraction methods. The processed data were then sent to machine learning classification models for training and realizing accurate gesture recognition. To verify the effectiveness of this system, we designed two groups of nine gestures in a hand-gesture recognition experiment. The results showed that the system can achieve a recognition accuracy of 98.3% with a group of four common gestures and an accuracy of 97.4% with a group of five pinch gestures. Additionally, two proof-of-concept interactive scenarios were implemented to demonstrate the general purpose of this system.