  In this paper the different properties of generalized Vaidya spacetime are
considered. We located and compared different types of horizons. We show that
the apparent horizon can contain the event horizon. The locations of all types
of horizons are compared with ones in usual Vaidya spacetime. Also, we consider
the conformal Killing vector and transform the metric to conformally-static
coordinates. We introduce a new constant of motion along null and timelike
geodesics, which is generated by homothetic Killing vector. The
conformally-static coordinates allow to diagonalize the generalized Vaidya
spacetime. The surface gravity has been calculated for the dust and stiff fluid
cases.
