Two new excited bands built on the πh11/2 configuration have been identified in 135Nd in addition to the known πh11/2 band. The energy spectra of the excited bands and the available electromagnetic transition probabilities are in good agreement with theoretical results obtained using quasiparticle-plus-triaxial-rotor model calculations. The properties of the bands identify them as tilted precession bands instead of wobbling bands. Our results give a new insight into the interpretation of the low-lying bands in odd-A mass nuclei, and can stimulate future studies to address the nuclear triaxiality.