ABSTRACT Blazars, a subclass of active galactic nuclei (AGN), are known to be bright γ-ray sources, frequently exhibiting active (flaring) periods. Blazar PKS 2155-304 is a high synchrotron-peaked BL Lac object located at redshift z = 0.116. On 2006 July 28, an extremely remarkable outburst of VHE γ-ray emission from this blazar was reported by the H.E.S.S. experiment, with an average flux more than 10 times the low-state level. The variability time-scale of this extraordinary flare was as short as approximately 200 s. In order to guarantee the transparency of the emission region for TeV photons, the fast variability demands an extremely high Doppler factor δD > 50 of the jet within the classical one-zone model, leading to the so-called ‘Doppler factor crisis’. Here, we demonstrate that the stochastic dissipation model, which is a multiblob scenario for blazars, can self-consistently explain the giant TeV flares of PKS 2155-304 and the low-state emission before and after the flares, in terms of both multiwavelength spectral and variability characteristics. The required Doppler factor in this model can be as low as 20, which is a reasonable and typical value for blazar jets. The obtained model parameters may shed some light on the physical properties of the relativistic jet.