Amide proton transfer (APT) imaging offers a novel and powerful MRI contrast mechanism for quantitative molecular imaging based on the principle of chemical exchange saturation transfer (CEST). Asymmetric magnetization transfer ratio (MTR(asym)) quantification is crucial for Z-spectrum analysis of APT imaging, but is still challenging, particularly at clinical field strength. This paper studies the accuracy and uncertainty in the quantification of MTR(asym) for APT imaging at 3T, by using high-order polynomial fitting of Z-spectrum through Monte Carlo simulation. Results show that polynomial fitting is a biased estimator that consistently underestimates MTR(asym). For a fixed polynomial order, the accuracy of MTR(asym) is almost constant with regard to signal-to-noise ratio (SNR) while the uncertainty decreases exponentially with SNR. The higher order polynomial fitting increases both the accuracy and the uncertainty of MTR(asym). For different APT signal intensity levels, the relative accuracy and the absolute uncertainty keep constant for a fixed polynomial order. These results indicate the limitations and pitfalls of polynomial fitting for MTR(asym) quantification so better quantification technique for MTR(asym) estimation is warranted.