New experimental results on the pressure dependence of magnetic susceptibility χ of SmS in semiconducting phase are obtained with precise measurements of χ as a function of the hydrostatic pressure P up to 2 kbar at liquid nitrogen and room temperatures. A pronounced magnitude of the pressure effect is found to be positive in sign and strongly temperature dependent: the pressure derivatives of χ, d lnχ/dP, are 6.3 ± 0.5 and 14.2 ± 1 Mbar−1 at 300 and 78 K, respectively. The experimental results are supplemented by theoretical calculations of the volume dependent electronic structure of SmS and orbital magnetism of the band electronic states χVV(band). It was found that χVV(band) value appeared to be strongly dependent on pressure, determining the main mechanism of the observed puzzling pressure effects in semiconducting SmS compound.