Gamma-ray burst ( GRB ) 120729A was detected by Swift /BAT and Fermi /GBM , and then rapidly observed by Swift /XRT , Swift /UVOT , and ground-based telescopes . It had a single long and smooth \gamma -ray emission pulse , which extends continuously to the X-rays . We report Lick/KAIT observations of the source , and make temporal and spectral joint fits of the multiwavelength light curves of GRB 120729A . It exhibits achromatic light-curve behavior , consistent with the predictions of the external shock model . The light curves are decomposed into four typical phases : onset bump ( Phase I ) , normal decay ( Phase II ) , shallow decay ( Phase III ) , and post-jet break ( Phase IV ) . The spectral energy distribution ( SED ) evolves from prompt \gamma -ray emission to the afterglow with photon index from \Gamma _ { \gamma } = 1.36 to \Gamma \approx 1.75 . There is no obvious evolution of the SED during the afterglow . The multiwavelength light curves from \gamma -ray to optical can be well modeled with an external shock by considering energy injection , and a time-dependent microphysics model with \epsilon _ { B } \propto t ^ { \alpha _ { B } } for the emission at early times , T < T _ { 0 } +157 s. Therefore , we conclude that both the prompt \gamma -ray emission and afterglow of GRB 120729A have the same external shock physical origin . Our model indicates that the \epsilon _ { B } evolution can be described as a broken power-law function with \alpha _ { B, 1 } = 0.18 \pm 0.04 and \alpha _ { B, 2 } = 0.84 \pm 0.04 . We also systematically investigate single-pulse GRBs in the Swift era , finding that only a small fraction of GRBs ( GRBs 120729A , 051111 , and 070318 ) are likely to originate from an external shock for both the prompt \gamma -ray emission and afterglow .