  In this paper, we studied the evolutions of the innermost stable circular
orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to
obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital
angular momentum. Then, we demonstrated this method is equivalent to the
effective potential method in general static and stationary spacetimes. Unlike
the effective potential method, which depends on the presence of the conserved
orbital energy, this method requires the existence of conserved orbital angular
momentum in spacetime. So it can be easily generalized to the dynamical
spacetimes where there exists conserved orbital angular momentum. From this
generalization, we studied the evolutions of the ISCOs in Vaidya spacetime,
Vaidya-AdS spacetime and the slow rotation limit of Kerr-Vaidya spacetime. The
results given by these examples are all reasonable and can be compared with the
evolutions of the photon spheres in dynamical spacetime
