The Kobe (Hyogo-ken Nanbu) earthquake (MS 6.8) occurred on 16 January 1995, in western Japan, bringing about a tremendous disaster. We constructed its source model by determining a spatio-temporal slip distribution using strong-motion seismograms recorded at a number of stations near the hypocenter. The source area is expressed using both a rough and a detailed subfault discretization system and a source-time function expanded with a finite number of basis functions at each subfault is determined. To perform stable inversions with many parameters, we construct a Bayesian model with unknown hyperparameters, incorporating prior constraints on the smoothness of spatio-temporal slip distribution in the observation equation. Using Akaike's Bayesian Information Criterion (ABIC), the optimal set of hyperparameters are objectively determined from observed data, which enables us to uniquely determine a spatio-temporal slip distribution. After rough analysis in which the actual rupture area is estimated as 45 × 20 km, we carried out a detailed analysis with a finer subfault discretization system (5 × 5 km). In our final source model, most of the slip exists beneath Awaji Island, and the rupture below the city of Kobe, where the damage was most serious, is relatively smaller. The large slips of about 2 m in the shallowest subfaults located southwest of the hypocenter correspond to the surface offsets observed along the Nojima fault. The overall focal mechanism of the source is right-lateral strike slip with a small thrust component, while total seismic moment is 2.0 × 1019 Nm. The source-time functions at shallow subfaults show a longer duration than those at deeper ones, being hypothesized to represent a possible combined effect of low rupture propagation velocity and varying friction behavior in shallow regions of crust.