In this paper, we studied the peak-to-peak output feedback control problem for a linear discrete-time system with input and output static quantizers, which are bounded by sectors. Firstly, the quantized peak-to-peak control issues are addressed with a robust problem by two sector-bound conditions. Secondly, by using linear fractional transformation (LFT) techniques, the closed-loop control system is expressed as an uncertain system with the LFT uncertainties. Then, we present sufficient conditions to design a peak-to-peak output feedback controller to mitigate quantization effects, and ensure a prescribed peak-to-peak noise attenuation level. Finally, two numerical examples are given to verify the effectiveness of the main results.