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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 thefrequency range from $5\times 10^{-9}$ to $2\times 10^{-7}$ Hz. Such signalscould be produced by individual supermassive binary black hole systems in theearly stage of coalescence. We phase up the pulsar timing array data set toform, for each position on the sky, two data streams that correspond to the twoGW polarizations and then carry out an optimal search for GW signals on thesedata streams. Since no statistically significant GWs were detected, we placeupper limits on the intrinsic GW strain amplitude $h_0$ for a range of GWfrequencies. For example, at $10^{-8}$ Hz our analysis has excluded with $95\%$confidence the presence of signals with $h_0\geqslant 1.7\times 10^{-14}$. Ournew limits are about a factor of four more stringent than those of Yardley etal. (2010) based on an earlier PPTA data set and a factor of two better thanthose reported in the recent Arzoumanian et al. (2014) paper. We also presentPPTA directional sensitivity curves and find that for the most sensitive regionon the sky, the current data set is sensitive to GWs from circular supermassivebinary black holes with chirp masses of $10^{9} M_{\odot}$ out to a luminositydistance of about 100 Mpc. Finally, we set an upper limit of $4 \times 10^{-3}{\rm{Mpc}}^{-3} {\rm{Gyr}}^{-1}$ at $95\%$ confidence on the coalescence rateof nearby ($z \lesssim 0.1$) supermassive binary black holes in circular orbitswith chirp masses of $10^{10}M_{\odot}$.

An all-sky search for continuous gravitational waves in the Parkes Pulsar Timing Array data set