Sitting is the most common status of modern human beings. Some sitting postures may bring health issues. To prevent the harm from bad sitting postures, a local sitting posture recognition system is desired with low power consumption and low computing overhead. The system should also provide good user experience with accuracy and privacy. This paper reports a novel posture recognition system on an office chair that can categorize seven different health-related sitting postures. The system uses six flex sensors, an Analog to Digital Converter (ADC) board and a Machine Learning algorithm of a two-layer Artificial Neural Network (ANN) implemented on a Spartan-6 Field Programmable Gate Array (FPGA). The system achieves 97.78% accuracy with a floating-point evaluation and 97.43% accuracy with the 9-bit fixed-point implementation. The ADC control logic and the ANN are constructed with a maximum propagation delay of 8.714 ns. The dynamic power consumption is 7.35 mW when the sampling rate is 5 Sample/second with the clock frequency of 5 MHz.