  Guided by the recent observational result that the meridional circulation of
the Sun becomes weaker at the time of the sunspot maximum, we have included a
parametric quenching of the meridional circulation in solar dynamo models such
that the meridional circulation becomes weaker when the magnetic field at the
base of the convection zone is stronger. We find that a flux transport solar
dynamo tends to become unstable on including this quenching of meridional
circulation if the diffusivity in the convection zone is less than about 2 *
10^{11} cm^2/s. The quenching of alpha, however, has a stabilizing effect and
it is possible to stabilize a dynamo with low diffusivity with sufficiently
strong alpha-quenching. For dynamo models with high diffusivity, the quenching
of meridional circulation does not produce a large effect and the dynamo
remains stable. We present a solar-like solution from a dynamo model with
diffusivity 2.8 * 10^{12} cm^2/s in which the quenching of meridional
circulation makes the meridional circulation vary periodically with solar cycle
as observed and does not have any other significant effect on the dynamo.
