High-temperature creep in fine-grained polycrystalline CaTiO3 perovskite was studied to get some insight into the rheology of the lower mantle. Polycrystalline specimens with grain-size ranging from 5 to 63 mu m were prepared by hot-pressing and subsequently deformed under room pressure or at 300 MPa confining pressure, temperatures of T = 1453-1573 K, and stresses of sigma = 6-100 MPa under the controlled oxygen fugacity of fO(2) = 0.24 x 10(5)-10(-10) Pa. Under all the tested conditions, the strain rate increases nearly linearly with stress and is inversely proportional to the second power of grain-size, a result consistent with the volume diffusion creep model. The comparison of the creep data with the diffusion coefficients and point defect models suggests that the diffusion of titanium or calcium ions through vacancy mechanism may be the rate-controlling process and that impurities play an important role. Both creep and grain-growth kinetics are shown to be significantly enhanced in the temperature range of T=1515-1525 K, presumably related to a structural phase transformation. A deformation mechanism map is constructed based on our data on diffusion creep and on the data on dislocation creep in coarse-grained polycrystals. Conditions under which diffusion creep dominates in CaTiO3 perovskite are wide which is presumably due to the role of twin boundaries to suppress dislocation creep but not diffusion creep. Assuming that the creep properties of (Mg, Fe)SiO3 perovskite are similar to CaTiO3 when compared at the same homologous temperature, the present results suggest that diffusion creep may dominate in a significant portion of the lower mantle and therefore significant rheological softening may occur associated with grain-size reduction after the transformation of spinel to perovskite + magnesiowustite. Also the structural phase transformation from the orthorhombic to higher symmetry structures (such as the tetragonal structure) in perovskite may reduce the creep strength.