  We investigate the relic abundance of asymmetric Dark Matter particles in
quintessence model with a kination phase. The analytic calculation of the
asymmetric Dark Matter in the standard cosmological scenario is extended to the
nonstandard cosmological scenario where we specifically discuss the
quintessence model with a kination phase. We found that the enhancement of
Hubble rate changes the relic density of particles and anti--particles. We use
the present day Dark Matter abundance to constrain the Hubble rate in
quintessence model with a kination phase for asymmetric Dark Matter.
