Recent observations have revealed that red, optically passive spiral galaxies with little or no optical emission lines, harbour significant amounts of dust-obscured star formation. We propose that these observational results can be explained if the spatial distributions of the cold gas and star-forming regions in these spiral galaxies are significantly more compact than those in blue star-forming spirals. Our numerical simulations show that if the sizes of star-forming regions in spiral galaxies with disc sizes of Rd are ~0.3Rd, such galaxies appear to have lower star formation rates as well as higher degrees of dust extinction. This is mainly because star formation in these spirals occurs only in the inner regions where both the gas densities and metallicities are higher, and hence the dust extinction is also significantly higher. We discuss whether star formation occurring preferentially in the inner regions of spirals is closely associated with the stripping of halo and disc gas via some sort of environmental effect. We suggest that the 'outside-in truncation of star formation' is the key to a better understanding of apparently optically passive spirals with dusty star-forming regions.