The purpose of this thesis is to design and implement an active noise cancellation headphone (ANC) with a feedback controller optimally designed using the linear quadratic regulator (LQR) design approach. The controller compares the audio input signal with the measured signal from a mini microphone in the headphone, and attempts to generate a control signal so that the headphone may reproduce a clean, low noise audio sound, without being interfered by the environmental noise. The control bandwidth of the ANC headphone is 100~600Hz. The controller design emphasizes the choice of a weighting function in shaping the controller gain at different frequencies, so as to achieve maximum in-band noise cancellation and low noise amplification outside the bandwidth. The experimental result shows achievable noise cancellation of maximum 25dB within the control bandwidth and a barely noticeable slight noise amplification of maximum 6dB at high frequencies and 4.5dB at inaudible low frequencies.