The five linear primary and secondary alcohols, i.e. n-propanol, isopropanol, n-butanol, 2-butanol and 2-pentanol, have similar chain lengths and slightly different structures. In this work, dielectric spectroscopy is used to investigate the properties of monohydroxy alcohols. The dielectric spectra of isopropanol and n-butanol show an abnormal change. i.e. the relaxation peaks with the highest strength gradually increases with temperature rising in a range of about 145–175 K. The analyses indicate that the abnormal variation originates from that of the Debye dielectric relaxation strength (DDRS) in the monohydroxy alcohols at above temperatures. According to the theoretical model of the DDRS for the monohydroxy alcohol, the abnormal variation is believed to be the result of the combined effects of decrease and increase of the DDRS caused by temperature, and the transformation of the structure of the hydrogen bonding molecular chain caused by the variation of the mobility of molecules. By comparing the relaxation times of the five monohydroxy alcohols, it is found that the conditions should be more stringent to cause the above-mentioned abnormal variation. In addition, the results also show that strength parameter of Debye processes, intrinsic vibration frequency of the relaxation units and their activation energy in the high-temperature limit in secondary alcohols also rise with the increase of the number of carbon atoms, similar to the scenario in the case of primary alcohols. These results can not only provide a new breakthrough point for the investigation of exotic properties in monohydroxy alcohols but also give a reference to explore the effect of molecular chain length on their dynamics.