The recent detection of cyanomethanimine in the interstellar medium makes its methyl derivative 2-iminopropanenitrile (CH_3_C(CN)NH) a promising candidate for an interstellar detection. The aim of this work is to extend the current knowledge of the laboratory rotational spectrum to higher frequencies, which is an essential prerequisite for an identification of the molecular species in the interstellar medium by millimetre-wave astronomy. The room-temperature rotational spectrum of 2-iminopropanenitrile has been measured in several frequency regions between 128 and 329GHz. The A-E splittings of the rotational transitions arising from the methyl top internal rotation were analysed employing the ERHAM and XIAM programs. A data set of approximately 900 newly assigned rotational transitions in the ground state of the Z isomer and a set of refined molecular constants including the internal rotation parameters are reported. Moreover, this work provides the first spectral characterisation of three lowest-lying vibrationally excited states v21=1, v14=1, and v20=1 of the Z isomer as well as of the less stable E isomer ground state. This comprehensive spectroscopic study will allow to search for 2-iminopropanenitrile in the millimetre-wave surveys of interstellar sources such as those recorded by the Atacama Large Millimeter/submillimeter Array.