Only limited data are available at present on the viscosity of kimberlite magmas. We investigate viscosity of synthetic carbonate-bearing (silicate82 + carbonate18, wt%, 100NBO/T = 313) anhydrous haplokimberlite melts theoretically and in experiments. We use new experimental data on viscosity of anhydrous haplokimberlite melts and a physical-chemical model (Persikov and Bukhtiyarov 2009; Persikov et al. 2015) to compare basic viscosity features in kimberlitic and basaltic melts (100NBO/T = 56). Viscosity of melts is determined by the falling sphere quenching method in a large range of temperatures from 1300 to 1950 °C and pressures up to 7.5 GPa. We use two types of high-pressure apparatuses: a high gas pressure apparatus and a high pressure split-sphere multi-anvil apparatus to study the viscosity of melts at moderate (100 MPa CO2 pressure) and high (5.5 GPa and 7.5 GPa) pressures, respectively. The measured viscosity ranges for anhydrous haplokimberlite melts are from 1.5 (±0.45) to 0.11(±0.03) Pa s. The temperature dependence of the viscosity of haplokimberlite and basaltic melts is consistent with the theoretical Arrhenian equation. At a constant temperature, viscosity of anhydrous haplokimberlite melts increases exponentially about ten-fold as pressure increases from 100 MPa to 7.5 GPa. The activation energy of viscous flow increases linearly with pressure increase from 100 MPa to 7.5 GPa for anhydrous haplokimberlite melts but decreases in the case of basaltic melts, with the minimum at ~5.5 GPa. At a moderate pressure (100 MPa), haplokimberlite melts are about twenty times less viscous than basaltic melts, but are about four times more viscous at a high pressure (7.5 GPa), the temperature being 1800 °C in both cases. The experimentally observed behavior of the viscosity of anhydrous haplokimberlite melts is consistent with predictions of the physical-chemical model within the range of uncertainties in both experimental and calculated data (±30% rel.). Thus, the physical-chemical model is used to discuss possible effects of volume percentages of crystals and bubbles on viscosity of kimberlitic and basaltic magmas at different pressures and temperatures during their origin, evolution, and ascent.