The sound velocity properties of single-crystal rhodochrosite (MnCO3) were determined up to 9.7GPa at ambient temperature by Brillouin scattering spectroscopy. Six elastic constants were calculated by a genetic algorithm method using the Christoffel's equations at each pressure. The elastic constants increased linearly as a function of pressure and its pressure derivatives Cij/P for C-11, C-33, C-44, C-12, C-13, C-14 were 5.86 (+/- 0.36), 3.82 (+/- 0.44), 2.06 (+/- 0.39), 5.07 (+/- 0.27), 5.34 (+/- 0.44), 1.52 (+/- 0.24), respectively. Based on the derived elastic constants of rhodochrosite, the aggregate adiabatic bulk and shear moduli (K-s and G) were calculated using the Voigt-Reuss-Hill averages and the linear fitting coefficients (K-s/P)(T) and (G/P)(T) were 5.05(+/- 0.26) and 0.73(+/- 0.05), respectively. The aggregate V-p of rhodochrosite increased clearly as a function of pressure and its pressure derivative V-p/P was 7.99(+/- 0.53)x10(-2)km/(sGPa), while the aggregate V-s increased slowly and V-s/P was only 1.19(+/- 0.12)x10(-2)km/(sGPa). The anisotropy factor for As of rhodochrosite increased from approximate to 40% at 0.8GPa to approximate to 48% at 9.7GPa, while A(p) decreased from approximate to 19% to approximate to 16% at the corresponding pressure.