We have studied the stability of low-degree g modes in uniformly rotating B-type stars, taking into account the effects of the Coriolis force and the rotational deformation. From an analysis treating rotation frequency as a small parameter, it is found that slow rotation tends to destabilize high-radial-order retrograde g modes, although the effect is very small or absent for relatively low-order modes. Calculating eigenfrequencies at selected rotation rates, we find, on the other hand, that rapid rotation tends to stabilize retrograde g modes. The stabilizing effect appears stronger for less-massive B-type stars having low effective temperatures. If we change the rotation rate continuously, the frequency of a g mode belonging to (ℓ, m) crosses frequencies of other g modes belonging to (ℓ′, m). If the parity of the two encountering modes is the same, then they interact with each other and the stability (i.e. imaginary part of eigenfrequency) of each mode is modified. Using an asymptotic method, we discuss the property of such mode crossings and couplings. For rapidly rotating stars, mode couplings are important for the stability of low-degree g modes. In particular, we find that the stabilization of retrograde g modes in rapidly rotating stars is due to many strong mode couplings, while prograde sectoral modes are exceptionally immune to the damping effects from the mode couplings.