We report results from a neutral hydrogen (H I) intensity mapping survey conducted with a Phased Array Feed (PAF) on the Parkes telescope.The survey was designed to cover ～ 380 deg2 over the redshift range 0.3 ＜ z ＜ 1 (a volume of ～ 1.5 Gpc3) in four fields covered by the WiggleZ Dark Energy Survey.The results presented here target a narrow redshift range of 0.73 ＜ z ＜ 0.78 where the effect of radio frequency interference (RFI) was less problematic.The data reduction and simulation pipeline was described,with an emphasis on flagging of RFI and correction for signal loss in the data reduction process,particularly due to the foreground subtraction methodology.A cross-correlation signal was detected between the H I intensity maps and the WiggleZ redshift data,with a mean amplitude of 〈△Tbδopt〉 =1.32-t-0.42 mK (statistical errors only).A future Parkes cryogenic PAF is expected to detect the cross-correlation signal with higher accuracy than previously possible and allow measurement of the cosmic H I density at redshifts up to unity.