  We study the zero-temperature phase transitions of a two-dimensional
disordered boson Hubbard model at incommensurate boson densities. Via matrix
diagonalization and quantum Monte Carlo simulations, we construct the phase
diagram and evaluate the correlation length exponent nu. In the presence of
weak disorder, we obtain nu=0.5 +- 0.1, the same value as that in the pure
model, near the tip of a Mott insulator lobe, using the dynamical critical
exponent z=2. As the strength of disorder is increased beyond a certain value,
however, the value of nu is found to change to 0.9 +- 0.1. This result strongly
suggests that there exist direct Mott insulator-to-superfluid transitions
around the tip of a Mott insulator lobe in the weak disorder regime.
