To remove the background signals from an IR spectrum is very useful and ideally all that remain in an IR spectrum are the desired absorption bands. Unfortunately, the removal of background bands is not always completely effective. In the present paper, an absorbance spectrum was obtained by scanning the same sample (polystyrene film or stearic acid KBr disc) both in background and sample single-beam measurements. It was found that a series of residual spikes appear in the strong absorption regions. The residuals are significantly different from that of random noise. There should be a nearly straight line according to theory analysis while spikes appear. Therefore those spikes are called anomalous absorption. The experimental results indicate that anomalous absorption is related to the absorbance of infrared bands. If the absorbance of an infrared band is lower than 1.0, anomalous absorption can be suppressed thoroughly. In addition, absorption anomalies can be substantially reduced by reducing the spectral resolution of the spectrum. The reasons for anomalous absorption were discussed and how to prevent the appearance of anomalous absorption by selecting appropriate background samples were suggested.