Utilizing the recursive equation of estimation of the constant gain α-β filter，the upper limit of the output estimation error is derived for coarse quantized input data. Numerical results of the upper limit of output estimation error for three different regions in the stable triangle of α-β filter are evaluated. Although the detail values of upper limit in respect to the three different regions are slightly different，numerical results express that the upper limit values of output estimation error are in the range of (0.5q～0.75q). Obviously，the computed upper limit values of output estimation error are always larger than the instantaneous values of output error; but the concept of this upper limit is useful for error analysis when input quantization error can not be treated as a white noise with uniform distribution.