We present results of an all-sky search in the Parkes Pulsar Timing Array (PPTA) Data Release 1 data set for continuous gravitational waves (GWs) in the frequency range from 5 × 10-9 to 2 × 10-7 Hz. Such signals could be produced by individual supermassive binary black hole systems in the early stage of coalescence.We phase up the pulsar timing array data set to form, for each position on the sky, two data streams that correspond to the twoGWpolarizations and then carry out an optimal search for GW signals on these data streams. Since no statistically significant GWs were detected, we place upper limits on the intrinsic GW strain amplitude h0 for a range of GW frequencies. For example, at 10-8 Hz our analysis has excluded with 95 per cent confidence the presence of signals with h0 ≥ 1.7 × 10-14. Our new limits are about a factor of 4 more stringent than those of Yardley et al. based on an earlier PPTA data set and a factor of 2 better than those reported in the recent Arzoumanian et al. paper.We also present PPTA directional sensitivity curves and find that for the most sensitive region on the sky, the current data set is sensitive to GWs from circular supermassive binary black holes with chirp masses of 109M⊙ out to a luminosity distance of about 100 Mpc. Finally, we set an upper limit of 4 × 10-3 Mpc-3 Gyr-1 at 95 per cent confidence on the coalescence rate of nearby (z ≲ 0.1) supermassive binary black holes in circular orbits with chirp masses of 1010M⊙.