During 2016 February, CSIRO Astronomy and Space Science and the Max-Planck-Institute for Radio Astronomy installed, commissioned, and carried out science observations with a phased array feed receiver system on the 64-m diameter Parkes radio telescope. Here, we demonstrate that the phased array feed can be used for pulsar observations and we highlight some unique capabilities. We demonstrate that the pulse profiles obtained using the phased array feed can be calibrated and that multiple pulsars can be simultaneously observed. Significantly, we find that an intrinsic polarisation leakage of −31 dB can be achieved with a phased array feed beam offset from the centre of the field of view. We discuss the possibilities for using a phased array feed for future pulsar observations and for searching for fast radio bursts with the Parkes and Effelsberg telescopes.