  We investigated a bulk viscous fluid universe with cosmological constant
{\Lambda} by assuming that the bulk viscosity to be proportional to the Hubble
parameter. We found that for an expanding universe, the (relative) matter
density will be always greater than a non-zero constant, and tends to this
non-zero constant in the future. We show that the bulk viscosity model has a
significantly better fitting to the combined SNeIa + CMB + BAO + H(z) data than
the {\Lambda}CDM model. Generally, the evolution or values of some cosmological
parameters predicted by the bulk viscosity model do not deviate significantly
from which are obtained from the {\Lambda}CDM model since the bulk viscosity
coefficient obtained from the astronomical observational data is so small. We
also made a statefinder analysis of the bulk viscosity model and found that the
evolution of the {r, s} parameters behaves in such a way that 0 < s < 1, 0.945
< r <1, indicating the bulk viscosity model is different from the {\Lambda}CDM
model.
